Quiz - physics - Systems of Particles and Rotational Motion-PYQ

Q1. The centre of mass of the system from the 5 kg particle is nearly at a distance of Source: orcusprep.in

NEET 2020

easy

(a) 33 cm

(b) 50 cm

(c) 67 cm

(d) 80 cm

Q2. Three masses are placed on the x-axis : 300 g at origin, 500 g at $x = 40 \text{ cm}$ and 400 g at $x = 70 \text{ cm}$. The distance of the centre of mass from the origin is Source: orcusprep.in

NEET 2012

easy

(a) 40 cm

(b) 45 cm

(c) 50 cm

(d) 30 cm

Q3. Two bodies of mass 1 kg and 3 kg have position vectors $\vec{r}_1 = \hat{i} + 2\hat{j} + \hat{k}$ and $\vec{r}_2 = -2\hat{i} - 2\hat{j} + \hat{k}$, respectively. The centre of mass of this system has a position vector Source: orcusprep.in

AIPMT 2009

medium

(a) $\frac{1}{4}(-\hat{i} + 4\hat{k})$

(b) $-\hat{i} - 2\hat{j} + 2\hat{k}$

(c) $\frac{1}{4}(-\hat{i} + 2\hat{j} + 2\hat{k})$

(d) $-\frac{1}{2}\hat{i} - \frac{1}{2}\hat{j} + \frac{1}{2}\hat{k}$

Q4. Consider a system of two particles having masses $m_1$ and $m_2$. If the particle of mass $m_1$ is pushed towards the centre of mass of the particles through a distance $d$, by what distance would be particle of mass $m_2$ move so as to keep the centre of mass of the particles at the original position ? Source: orcusprep.in

AIPMT 2004

medium

(a) $\frac{m_1}{m_1 + m_2}d$

(b) $\frac{m_1}{m_2}d$

(c) $d$

(d) $\frac{m_2}{m_1}d$

Q5. Three identical metal balls, each of radius $r$ are placed touching each other on a horizontal surface such that an equilateral triangle is formed when centres of three balls are joined. The centre of the mass of the system is located at Source: orcusprep.in

AIPMT 1999

easy

(a) line joining centres of any two balls

(b) centre of one of the balls

(c) horizontal surface

(d) point of intersection of the medians.

Q6. The centre of mass of system of particles does not depend on Source: orcusprep.in

AIPMT 1997

easy

(a) position of the particles

(b) relative distances between the particles

(c) masses of the particles

(d) forces acting on the particle.

Q7. Two persons of masses 55 kg and 65 kg respectively, are at the opposite ends of a boat. The length of the boat is $3.0 \text{ m}$ and weighs 100 kg. The 55 kg man walks up to the 65 kg man and sits with him. If the boat is in still water the center of mass of the system shifts by Source: orcusprep.in

NEET 2012

medium

(a) $3.0 \text{ m}$

(b) $2.3 \text{ m}$

(c) zero

(d) $0.75 \text{ m}$

Q8. Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are $v$ and $2v$ at any instant, then the speed of centre of mass of the system will be Source: orcusprep.in

AIPMT 2010

easy

(a) $2v$

(b) zero

(c) $1.5v$

(d) $v$

Q9. A man of 50 kg mass is standing in a gravity free space at a height of $10 \text{ m}$ above the floor. He throws a stone of $0.5 \text{ kg}$ mass downwards with a speed $2 \text{ m/s}$. When the stone reaches the floor, the distance of the man above the floor will be Source: orcusprep.in

AIPMT 2010

medium

(a) $9.9 \text{ m}$

(b) $10.1 \text{ m}$

(c) $10 \text{ m}$

(d) $20 \text{ m}$

Q10. Vectors, $\vec{A}$, $\vec{B}$, and $\vec{C}$ are such that $\vec{A} \cdot \vec{B} = 0$ and $\vec{A} \cdot \vec{C} = 0$ . Then the vector parallel to $\vec{A}$ is Source: orcusprep.in

NEET 2013

medium

(a) $\vec{A} \times \vec{B}$

(b) $\vec{B} + \vec{C}$

(c) $\vec{B} \times \vec{C}$

(d) $\vec{B}$ and $\vec{C}$

Q11. $\vec{A}$ and $\vec{B}$ are two vectors and $\theta$ is the angle between them, if $\mid \vec{A} \times \vec{B} \mid = \sqrt{3} (\vec{A} \cdot \vec{B})$, the value of $\theta$ is Source: orcusprep.in

AIPMT 2007

easy

(a) $45^{\degree}$

(b) $30^{\degree}$

(c) $90^{\degree}$

(d) $60^{\degree}$

Q12. If the angle between the vectors $\vec{A}$ and $\vec{B}$ is $\theta$, the value of the product $(\vec{B} \times \vec{A}) \cdot \vec{A}$ is equal to Source: orcusprep.in

AIPMT 2005

medium

(a) $BA^2 \sin\theta$

(b) $BA^2 \cos\theta$

(c) $BA^2 \sin\theta \cos\theta$

(d) zero.

Q13. If $\mid \vec{A} \times \vec{B} \mid = \sqrt{3} \vec{A} \cdot \vec{B}$ then the value of $\mid \vec{A} + \vec{B} \mid$ is Source: orcusprep.in

AIPMT 2004

hard

(a) $\left(A^2 + B^2 + AB\right)^{1/2}$

(b) $\left(A^2 + B^2 + \frac{AB}{3}\right)^{1/2}$

(c) $A + B$

(d) $\left(A^2 + B^2 + AB/\sqrt{3}\right)^{1/2}$

Q14. The resultant of $\vec{A} \times \vec{0}$ will be equal to Source: orcusprep.in

AIPMT 1992

easy

(a) zero

(b) $A$

(c) zero vector

(d) unit vector.

Q15. What is the value of linear velocity, if $\vec{r} = -3\hat{i} + 4\hat{j} + \hat{k}$ and $\vec{\omega} = 5\hat{i} - 6\hat{j} + 6\hat{k}$ ? Source: orcusprep.in

NEET 1999

medium

$4\hat{i} + \hat{j} + 36\hat{k}$

$18\hat{i} + 13\hat{j} - 2\hat{k}$

$6\hat{i} + 2\hat{j} - 3\hat{k}$

$6\hat{i} - 2\hat{j} + 8\hat{k}$

Q16. Find the torque about the origin when a force of $3\hat{j}\text{ N}$ acts on a particle whose position vector is $2\hat{k}\text{ m}$. Source: orcusprep.in

NEET 2020

easy

$6\hat{i}\text{ N}\cdot\text{m}$

$6\hat{j}\text{ N}\cdot\text{m}$

$-6\hat{i}\text{ N}\cdot\text{m}$

$6\hat{k}\text{ N}\cdot\text{m}$

Q17. The moment of the force, $\vec{F} = 4\hat{i} + 5\hat{j} - 6\hat{k}$ at $(2, 0, -3)$, about the point $(2, -2, -2)$, is given by Source: orcusprep.in

NEET 2018

medium

$-8\hat{i} - 4\hat{j} - 7\hat{k}$

$-4\hat{i} - 8\hat{j} - \hat{k}$

$-7\hat{i} - 8\hat{j} - 4\hat{k}$

$-7\hat{i} - 4\hat{j} - 8\hat{k}$

Q18. A force $\vec{F} = \alpha\hat{i} + 3\hat{j} + 6\hat{k}$ is acting at a point $\vec{r} = 2\hat{i} - 6\hat{j} - 12\hat{k}$. The value of $\alpha$ for which angular momentum about origin is conserved is Source: orcusprep.in

NEET 2015

medium

zero

1

$-1$

2

Q19. A mass $m$ moves in a circle on a smooth horizontal plane with velocity $v_0$ at a radius $R_0$. The mass is attached to a string which passes through a smooth hole in the plane as shown. The tension in the string is increased gradually and finally $m$ moves in a circle of radius $\frac{R_0}{2}$. The final value of the kinetic energy is image_here Source: orcusprep.in

NEET 2015 Cancelled

medium

$2 m v_0^2$

$\frac{1}{2} m v_0^2$

$m v_0^2$

$\frac{1}{4} m v_0^2$

Q20. When a mass is rotating in a plane about a fixed point, its angular momentum is directed along Source: orcusprep.in

NEET 2012

easy

a line perpendicular to the plane of rotation

the line making an angle of $45\degree$ to the plane of rotation

the radius

the tangent to the orbit.

Q21. A small mass attached to a string rotates on a frictionless table top as shown. If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2, the kinetic energy of the mass will Source: orcusprep.in

NEET Mains 2011

medium

decrease by a factor of 2

remain constant

increase by a factor of 2

increase by a factor of 4

Q22. If $\vec{F}$ is the force acting on a particle having position vector $\vec{r}$ and $\vec{\tau}$ be the torque of this force about the origin, then Source: orcusprep.in

NEET 2009

easy

$\vec{r} \cdot \vec{\tau} > 0$ and $\vec{F} \cdot \vec{\tau} < 0$

$\vec{r} \cdot \vec{\tau} = 0$ and $\vec{F} \cdot \vec{\tau} = 0$

$\vec{r} \cdot \vec{\tau} = 0$ and $\vec{F} \cdot \vec{\tau} \ne 0$

$\vec{r} \cdot \vec{\tau} \ne 0$ and $\vec{F} \cdot \vec{\tau} = 0$

Q23. A particle of mass $m$ moves in the XY plane with a velocity $v$ along the straight line AB. If the angular momentum of the particle with respect to origin O is $L_A$ when it is at A and $L_B$ when it is at B, then Source: orcusprep.in

NEET 2007

easy

$L_A = L_B$

the relationship between $L_A$ and $L_B$ depends upon the slope of the line AB

$L_A < L_B$

$L_A > L_B$

Q24. Find the torque of a force $\vec{F} = -3\hat{i} + 5\hat{j} + \hat{k}$ acting at the point $\vec{r} = 7\hat{i} + 3\hat{j} + \hat{k}$. Source: orcusprep.in

NEET 1997

medium

$-2\hat{i} + 14\hat{j} + 4\hat{k}$

$-14\hat{i} + 34\hat{j} - 16\hat{k}$

$-2\hat{i} - 10\hat{j} + 44\hat{k}$

$4\hat{i} + 4\hat{j} + 6\hat{k}$

Q25. What is the torque of the force $\vec{F} = 2\hat{i} - 3\hat{j} + 4\hat{k}\text{ N}$ acting at the point $\vec{r} = 3\hat{i} + 2\hat{j} + 3\hat{k}\text{ m}$ about origin? Source: orcusprep.in

NEET 1995

medium

$-6\hat{i} + 6\hat{j} - 12\hat{k}$

$-17\hat{i} + 6\hat{j} + 13\hat{k}$

$6\hat{i} - 6\hat{j} + 12\hat{k}$

$17\hat{i} - 6\hat{j} - 13\hat{k}$

Q26. A particle of mass $m = 5$ is moving with a uniform speed $v = 3\sqrt{2}$ in the XOY plane along the line $y = x + 4$. The magnitude of the angular momentum of the particle about the origin is Source: orcusprep.in

NEET 1991

medium

60 units

$40\sqrt{2}$ units

zero

7.5 units

Q27. Which of the following statements are correct? (1) Centre of mass of a body always coincides with the centre of gravity of the body. (2) Centre of mass of a body is the point at which the total gravitational torque on the body is zero. (3) A couple on a body produces both translational and rotational motion in a body. (4) Mechanical advantage greater than one means that small effort can be used to lift a large load. Source: orcusprep.in

NEET 2017

medium

(1) and (2)

(2) and (3)

(3) and (4)

(2) and (4)

Q28. A rod of weight $W$ is supported by two parallel knife edges A and B and is in equilibrium in a horizontal position. The knives are at a distance $d$ from each other. The centre of mass of the rod is at distance $x$ from A. The normal reaction on A is Source: orcusprep.in

NEET 2015 Cancelled

medium

$W \frac{d-x}{x}$

$W \frac{d-x}{d}$

$\frac{W x}{d}$

$\frac{W d}{x}$

Q29. ABC is an equilateral triangle with O as its centre. $\vec{F}_1, \vec{F}_2, \vec{F}_3$ represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is zero then the magnitude of $\vec{F}_3$ is image_here Source: orcusprep.in

NEET 2012, 1998

medium

$F_1 + F_2$

$F_1 - F_2$

$\frac{F_1 + F_2}{2}$

$2(F_1 + F_2)$

Q30. Centre of gravity (C.G.) of a body is the point at which the weight of the body acts. Centre of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius. To evaluate the gravitational field intensity due to any body at an external point, the entire mass of the body can be considered to be concentrated at its C.G. The radius of gyration of any body rotating about an axis is the length of the perpendicular drawn from the C.G. of the body to the axis. Which one of the following pairs of statements is correct? Source: orcusprep.in

NEET Mains 2010

medium

(4) and (1)

(1) and (2)

(2) and (3)

(3) and (4)

Q31. A rod of length $3\text{ m}$ and its mass per unit length is directly proportional to distance $x$ from one of its end then its centre of gravity from that end will be at Source: orcusprep.in

NEET 2002

medium

$1.5\text{ m}$

$2\text{ m}$

$2.5\text{ m}$

$3.0\text{ m}$

Q32. 250 N force is required to raise 75 kg mass from a pulley. If rope is pulled 12 m then the load is lifted to 3 m, the efficiency of pulley system will be Source: orcusprep.in

NEET 2001

medium

25%

33.3%

75%

90%

Q33. A couple produces Source: orcusprep.in

NEET 1997

easy

linear and rotational motion

no motion

purely linear motion

purely rotational motion.

Q34. A solid sphere of mass $m$ and radius $R$ is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation ($E_{sphere}/E_{cylinder}$) will be Source: orcusprep.in

NEET 2016

medium

2 : 3

1 : 5

1 : 4

3 : 1

Q35. A light rod of length $l$ has two masses $m_1$ and $m_2$ attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is Source: orcusprep.in

NEET 2016

medium

$\frac{m_1m_2}{m_1+m_2}l^2$

$\frac{m_1m_2}{m_1+m_2}l$

$(m_1 + m_2)l^2$

$\sqrt{m_1m_2}l^2$

Q36. From a circular disc of radius $R$ and mass $9M$, a small disc of mass $M$ and radius $R/3$ is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is Source: orcusprep.in

AIPMT 2010

hard

$\frac{40}{9}MR^2$

$MR^2$

$4MR^2$

$\frac{4}{9}MR^2$

Q37. The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is Source: orcusprep.in

AIPMT 2008

easy

$\sqrt{2}:1$

$\sqrt{2}:\sqrt{3}$

$\sqrt{3}:\sqrt{2}$

$1:\sqrt{2}$

Q38. Two bodies have their moments of inertia $I$ and $2I$ respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular velocity will be in the ratio Source: orcusprep.in

AIPMT 2005

easy

$\sqrt{2}:1$

$1:2$

$2:1$

$1:\sqrt{2}$

Q39. Three particles, each of mass $m$ gram, are situated at the vertices of an equilateral triangle ABC of side $l$ cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram-cm$^2$ units will be Source: orcusprep.in

AIPMT 2004

medium

$\frac{3}{4}ml^2$

$2ml^2$

$\frac{5}{4}ml^2$

$\frac{3}{2}ml^2$

Q40. A fly wheel rotating about fixed axis has a kinetic energy of 360 joule when its angular speed is 30 radian/sec. The moment of inertia of the wheel about the axis of rotation is Source: orcusprep.in

AIPMT 1990

easy

0.6 kg m$^2$

0.15 kg m$^2$

0.8 kg m$^2$

0.75 kg m$^2$

Q41. A ring of mass $m$ and radius $r$ rotates about an axis passing through its centre and perpendicular to its plane with angular velocity $\omega$. Its kinetic energy is Source: orcusprep.in

AIPMT 1988

easy

$\frac{1}{2}mr^2\omega^2$

$mr\omega^2$

$mr^2\omega^2$

$\frac{1}{2}mr\omega$

Q42. From a disc of radius $R$ and mass $M$, a circular hole of diameter $R$, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre? Source: orcusprep.in

NEET 2016

hard

$\frac{11}{32}MR^2$

$\frac{9}{32}MR^2$

$\frac{15}{32}MR^2$

$\frac{13}{32}MR^2$

Q43. Three identical spherical shells, each of mass $m$ and radius $r$ are placed as shown in figure. Consider an axis $XX^\prime$ which is touching the two shells and passing through the diameter of the third shell. Moment of inertia of the system consisting of these three spherical shells about $XX^\prime$ axis is Source: orcusprep.in

NEET 2015

hard

$\frac{16}{5}mr^2$

$4mr^2$

$\frac{11}{5}mr^2$

$3mr^2$

Q44. The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through Source: orcusprep.in

AIPMT 2012

easy

B

C

D

A

Q45. The moment of inertia of a thin uniform rod of mass $M$ and length $L$ about an axis passing through its midpoint and perpendicular to its length is $I_0$. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is Source: orcusprep.in

AIPMT 2011

medium

$I_0 + \frac{ML^2}{2}$

$I_0 + \frac{ML^2}{4}$

$I_0 + 2ML^2$

$I_0 + ML^2$

Q46. Four identical thin rods each of mass $M$ and length $l$, form a square frame. Moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is Source: orcusprep.in

AIPMT 2009

medium

$\frac{2}{3}Ml^2$

$\frac{13}{3}Ml^2$

$\frac{1}{3}Ml^2$

$\frac{4}{3}Ml^2$

Q47. A thin rod of length $L$ and mass $M$ is bent at its midpoint into two halves so that the angle between them is $90^\circ$. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is Source: orcusprep.in

AIPMT 2008

hard

$\frac{ML^2}{6}$

$\frac{\sqrt{2}ML^2}{24}$

$\frac{ML^2}{24}$

$\frac{ML^2}{12}$

Q48. The moment of inertia of a uniform circular disc of radius $R$ and mass $M$ about an axis touching the disc at its diameter and normal to the disc Source: orcusprep.in

AIPMT 2006

medium

$\frac{1}{2}MR^2$

$MR^2$

$\frac{2}{5}MR^2$

$\frac{3}{2}MR^2$

Q49. The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius and mass about a tangential axis in the plane of the ring is Source: orcusprep.in

AIPMT 2004

medium

2 : 3

2 : 1

$\sqrt{5} : \sqrt{6}$

$1 : \sqrt{2}$

Q50. The moment of inertia of a disc of mass M and radius R about an axis, which is tangential to the circumference of the disc and parallel to its diameter is Source: orcusprep.in

AIPMT 1999

medium

$\frac{5}{4}MR^2$

$\frac{2}{3}MR^2$

$\frac{3}{2}MR^2$

$\frac{4}{5}MR^2$

Q51. Moment of inertia of a uniform circular disc about a diameter is I. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be Source: orcusprep.in

AIPMT 1990

medium

5I

3I

6I

4I

Q52. A wheel has angular acceleration of 3.0 rad/sec$^2$ and an initial angular speed of 2.00 rad/sec. In a time of 2 sec it has rotated through an angle (in radians) of Source: orcusprep.in

AIPMT 2007

easy

10

12

4

6

Q53. A solid cylinder of mass 2 kg and radius 4 cm is rotating about its axis at the rate of 3 rpm. The torque required to stop it after $2\pi$ revolutions is Source: orcusprep.in

NEET 2019

medium

$2 \times 10^6$ N m

$2 \times 10^{-6}$ N m

$2 \times 10^{-3}$ N m

$12 \times 10^{-4}$ N m

Q54. Three objects, A: (a solid sphere), B: (a thin circular disk) and C: (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed $\omega$ about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation Source: orcusprep.in

NEET 2018

medium

$W_C > W_B > W_A$

$W_A > W_B > W_C$

$W_B > W_A > W_C$

$W_A > W_C > W_B$

Q55. A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N? Source: orcusprep.in

NEET 2017

medium

0.25 rad s$^{-2}$

25 rad s$^{-2}$

5 m s$^{-2}$

25 m s$^{-2}$

Q56. A uniform circular disc of radius 50 cm at rest is free to turn about an axis which is perpendicular to its plane and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of 2.0 rad s$^{-2}$. Its net acceleration in m s$^{-2}$ at the end of 2.0 s is approximately Source: orcusprep.in

NEET 2016

medium

6.0

3.0

8.0

7.0

Q57. Point masses $m_1$ and $m_2$ are placed at the opposite ends of a rigid rod of length L, and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity $\omega_0$ is minimum, is given by Source: orcusprep.in

NEET 2015

hard

$x = \frac{m_2}{m_1}L$

$x = \frac{m_2 L}{m_1 + m_2}$

$x = \frac{m_1 L}{m_1 + m_2}$

$x = \frac{m_1}{m_2}L$

Q58. An automobile moves on a road with a speed of 54 km h$^{-1}$. The radius of its wheels is 0.45 m and the moment of inertia of the wheel about its axis of rotation is 3 kg m$^2$. If the vehicle is brought to rest in 15 s, the magnitude of average torque transmitted by its brakes to the wheel is Source: orcusprep.in

NEET 2015

medium

10.86 kg m$^2$ s$^{-2}$

2.86 kg m$^2$ s$^{-2}$

6.66 kg m$^2$ s$^{-2}$

8.58 kg m$^2$ s$^{-2}$

Q59. A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions s$^{-2}$ is Source: orcusprep.in

NEET 2014

medium

25 N

50 N

78.5 N

157 N

Q60. A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is Source: orcusprep.in

NEET 2013

medium

$\frac{2g}{L}$

$\frac{2g}{L^2}$

$\frac{3g}{2L}$

$\frac{g}{L}$

Q61. The instantaneous angular position of a point on a rotating wheel is given by the equation $\theta(t) = 2t^3 - 6t^2$. The torque on the wheel becomes zero at Source: orcusprep.in

AIPMT 2011

medium

t = 1 s

t = 0.5 s

t = 0.25 s

t = 2 s

Q62. A uniform rod AB of length l and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A is $ml^2/3$, the initial angular acceleration of the rod will be Source: orcusprep.in

AIPMT 2007

medium

$\frac{mgl}{2}$

$\frac{3gl}{2}$

$\frac{3g}{2l}$

$\frac{2g}{3l}$

Q63. A wheel having moment of inertia 2 kg m$^2$ about its vertical axis, rotates at the rate of 60 rpm about this axis. The torque which can stop the wheel's rotation in one minute would be Source: orcusprep.in

AIPMT 2004

medium

$\frac{2\pi}{15}$ N m

$\frac{\pi}{12}$ N m

$\frac{\pi}{15}$ N m

$\frac{\pi}{18}$ N m

Q64. The moment of inertia of a body about a given axis is 1.2 kg m$^2$. Initially, the body is at rest. In order to produce a rotational kinetic energy of 1500 joule, an angular acceleration of 25 radian/sec$^2$ must be applied about that axis for a duration of Source: orcusprep.in

AIPMT 1990

medium

4 s

2 s

8 s

10 s

Q65. A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere? Source: orcusprep.in

NEET 2018

easy

Angular velocity

Moment of inertia

Rotational kinetic energy

Angular momentum

Q66. Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc has angular velocities $\omega_1$ and $\omega_2$. They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is Source: orcusprep.in

NEET 2017

hard

$\frac{1}{4}I(\omega_1 - \omega_2)^2$

$I(\omega_1 - \omega_2)^2$

$\frac{1}{8}I(\omega_1 - \omega_2)^2$

$\frac{1}{2}I(\omega_1 + \omega_2)^2$

Q67. Two rotating bodies A and B of masses m and 2m with moments of inertia $I_A$ and $I_B$ ($I_B > I_A$) have equal kinetic energy of rotation. If $L_A$ and $L_B$ be their angular momenta respectively, then Source: orcusprep.in

NEET 2016

medium

$\frac{L_A}{L_B} = 2$

$L_A = 2L_B$

$L_B > L_A$

$L_A > L_B$

Q68. Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc $D_1$ has 2 kg mass and 0.2 m radius and initial angular velocity of 50 rad s$^{-1}$. Disc $D_2$ has 4 kg mass, 0.1 m radius and initial angular velocity of 200 rad s$^{-1}$. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in rad s$^{-1}$) of the system is Source: orcusprep.in

NEET 2013

hard

60

100

120

40

Q69. A circular platform is mounted on a frictionless vertical axle. Its radius R = 2 m and its moment of inertia about the axle is 200 kg m$^2$. It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of 1 m s$^{-1}$ relative to the ground. Time taken by the man to complete one revolution is Source: orcusprep.in

AIPMT 2012

hard

$\pi$ s

$\frac{3\pi}{2}$ s

$2\pi$ s

$\frac{\pi}{2}$ s

Q70. A circular disk of moment of inertia $I_t$ is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed $\omega_i$. Another disk of moment of inertia $I_b$ is dropped coaxially onto the rotating disk. Initially the second disk has zero angular speed. Eventually both the disks rotate with a constant angular speed $\omega_f$. The energy lost by the initially rotating disc to friction is Source: orcusprep.in

AIPMT 2010

hard

$\frac{1}{2}\frac{I_b^2}{(I_t + I_b)}\omega_i^2$

$\frac{1}{2}\frac{I_t^2}{(I_t + I_b)}\omega_i^2$

$\frac{I_b I_t}{(I_t + I_b)}\omega_i^2$

$\frac{1}{2}\frac{I_b I_t}{(I_t + I_b)}\omega_i^2$

Q71. A thin circular ring of mass M and radius r is rotating about its axis with constant angular velocity $\omega$. Two objects each of mass m are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity given by Source: orcusprep.in

AIPMT 2010

medium

$\frac{(M + 2m)\omega}{2m}$

$\frac{2M\omega}{M + 2m}$

$\frac{(M + 2m)\omega}{M}$

$\frac{M\omega}{M + 2m}$

Q72. A round disc of moment of inertia $I_2$ about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia $I_1$ rotating with an angular velocity $\omega$ about the same axis. The final angular velocity of the combination of discs is Source: orcusprep.in

AIPMT 2004

medium

$\frac{I_2\omega}{I_1 + I_2}$

$\omega$

$\frac{I_1\omega}{I_1 + I_2}$

$\frac{(I_1 + I_2)\omega}{I_1}$

Q73. A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity $\omega$. Four objects each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be Source: orcusprep.in

AIPMT 2003

medium

$\frac{M\omega}{4m}$

$\frac{M\omega}{M + 4m}$

$\frac{(M + 4m)\omega}{M}$

$\frac{(M - 4m)\omega}{M + 4m}$

Q74. A disc is rotating with angular speed $\omega$. If a child sits on it, what is conserved? Source: orcusprep.in

AIPMT 2002

easy

Linear momentum

Angular momentum

Kinetic energy

Potential energy

Q75. A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its centre of mass has speed of 20 cm/s. How much work is needed to stop it? Source: orcusprep.in

NEET 2019

medium

1 J

3 J

30 kJ

2 J

Q76. A solid cylinder of mass 2 kg and radius 50 cm rolls up an inclined plane of angle inclination 30°. The centre of mass of cylinder has speed of 4 m/s. The distance travelled by the cylinder on the incline surface will be (Take g = 10 m/s$^2$) Source: orcusprep.in

NEET 2019

medium

2.2 m

1.6 m

1.2 m

2.4 m

Q77. A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy ($K_t$) as well as rotational kinetic energy ($K_r$) simultaneously. The ratio $K_t : (K_t + K_r)$ for the sphere is Source: orcusprep.in

NEET 2018

medium

7 : 10

5 : 7

10 : 7

2 : 5

Q78. A disc and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first? Source: orcusprep.in

NEET 2016

medium

Both reach at the same time

Depends on their masses

Disc

Sphere

Q79. The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle $\theta$ without slipping and slipping down the incline without rolling is Source: orcusprep.in

NEET 2014

medium

5 : 7

2 : 3

2 : 5

7 : 5

Q80. A small object of uniform density rolls up a curved surface with an initial velocity $v$. It reaches upto a maximum height of $\frac{3v^2}{4g}$ with respect to the initial position. The object is Source: orcusprep.in

NEET 2013

hard

Hollow sphere

Disc

Ring

Solid sphere

Q81. A solid cylinder of mass 3 kg is rolling on a horizontal surface with velocity 4 m s$^{-1}$. It collides with a horizontal spring of force constant 200 N m$^{-1}$. The maximum compression produced in the spring will be Source: orcusprep.in

NEET 2012

medium

0.5 m

0.6 m

0.7 m

0.2 m

Q82. A solid cylinder and a hollow cylinder, both of the same mass and same external diameter are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first? Source: orcusprep.in

AIPMT 2010

medium

Both together only when angle of inclination of plane is 45°

Both together

Hollow cylinder

Solid cylinder

Q83. A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle $\theta$. The frictional force Source: orcusprep.in

AIPMT 2005

medium

dissipates energy as heat

decreases the rotational motion

decreases the rotational and translational motion

converts translational energy to rotational energy

Q84. A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is K. If radius of the ball be R, then the fraction of total energy associated with its rotational energy will be Source: orcusprep.in

AIPMT 2003

medium

$\frac{K^2 + R^2}{R^2}$

$\frac{K^2}{R^2}$

$\frac{K^2}{K^2 + R^2}$

$\frac{R^2}{K^2 + R^2}$

Q85. A solid cylinder of mass M and radius R rolls without slipping down an inclined plane of length L and height h. What is the speed of its centre of mass when the cylinder reaches its bottom? Source: orcusprep.in

AIPMT 2003

medium

$\sqrt{2gh}$

$\sqrt{\frac{3}{4}gh}$

$\sqrt{\frac{4}{3}gh}$

$\sqrt{4gh}$

Q86. Consider a contact point P of a wheel on ground which rolls on ground without slipping. Then value of displacement of point P when wheel completes half of rotation (If radius of wheel is 1 m) Source: orcusprep.in

AIPMT 2002

hard

2 m

$\sqrt{\pi^2 + 4}$ m

$\pi$ m

$\sqrt{\pi^2 + 2}$ m

Q87. A solid sphere of radius R is placed on a smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of centre of mass, which is correct? Source: orcusprep.in

AIPMT 2002

medium

h = R

h = 2R

h = 0

no relation between h and R

Q88. A disc is rolling, the velocity of its centre of mass is $v_{cm}$. Which one will be correct? Source: orcusprep.in

AIPMT 2001

easy

The velocity of highest point is $2v_{cm}$ and at point of contact is zero

The velocity of highest point is $v_{cm}$ and at point of contact is $v_{cm}$

The velocity of highest point is $2v_{cm}$ and point of contact is $v_{cm}$

The velocity of highest point is $2v_{cm}$ and point of contact is $2v_{cm}$

Q89. A solid spherical ball rolls on a table. Ratio of its rotational kinetic energy to total kinetic energy is Source: orcusprep.in

AIPMT 1994

medium

1/2

1/6

7/10

2/7

Q90. A solid sphere, disc and solid cylinder all of the same mass and radius are allowed to roll down (from rest) on the inclined plane, then Source: orcusprep.in

AIPMT 1993

medium

solid sphere reaches the bottom first

solid sphere reaches the bottom last

disc will reach the bottom first

all reach the bottom at the same time

Q91. The speed of a homogenous solid sphere after rolling down an inclined plane of vertical height h from rest without sliding is Source: orcusprep.in

AIPMT 1992

medium

$\sqrt{\frac{10}{7}gh}$

$\sqrt{gh}$

$\sqrt{\frac{6}{5}gh}$

$\sqrt{\frac{4}{3}gh}$

Q92. A solid homogenous sphere of mass M and radius is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of the sphere Source: orcusprep.in

AIPMT 1988

hard

total kinetic energy is conserved

the angular momentum of the sphere about the point of contact with the plane is conserved

only the rotational kinetic energy about the centre of mass is conserved

angular momentum about the centre of mass is conserved

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Physics - Systems of Particles and Rotational Motion-PYQ

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Physics - Systems of Particles and Rotational Motion-PYQ

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