Quiz - physics - Work Power & Energy-PYQ

Q1. A particle moves so that its position vector is given by $\mathbf{\vec{r}(t) = \hat{i} \cos (\omega t) + \hat{j} \sin (\omega t)}$, where $\omega$ is a constant. Which of the following is true? Source: orcusprep.in

NEET 2016

medium

Velocity is perpendicular to $\mathbf{\vec{r}}$ and acceleration is directed towards the origin.

Velocity is perpendicular to $\mathbf{\vec{r}}$ and acceleration is directed away from the origin.

Velocity and acceleration both are perpendicular to $\mathbf{\vec{r}}$.

Velocity and acceleration both are parallel to $\mathbf{\vec{r}}$.

Q2. A particle moves from a point $\mathbf{(-2\hat{i} + 5\hat{j})}$ to $\mathbf{(4\hat{j} + 3\hat{k})}$ when a force of $\mathbf{(4\hat{i} + 3\hat{j})\ \text{N}}$ is applied. How much work has been done by the force? Source: orcusprep.in

NEET 2016

easy

$8\ \text{J}$

$11\ \text{J}$

$5\ \text{J}$

$2\ \text{J}$

Q3. If vectors $\mathbf{\vec{A}(t) = \hat{i} \cos (\omega t) + \hat{j} \sin (\omega t)}$ and $\mathbf{\vec{B}(t) = \hat{i} \cos (\frac{\omega t}{2}) + \hat{j} \sin (\frac{\omega t}{2})}$ are functions of time, then the value of $t$ at which they are orthogonal to each other is Source: orcusprep.in

NEET 2015

medium

$t = \frac{\pi}{\omega}$

$t = 0$

$t = \frac{\pi}{4\omega}$

$t = \frac{\pi}{2\omega}$

Q4. If a vector $\mathbf{2\hat{i} + 3\hat{j} + 8\hat{k}}$ is perpendicular to the vector $\mathbf{4\hat{i} - 4\hat{j} + \alpha\hat{k}}$, then the value of $\alpha$ is Source: orcusprep.in

AIPMT 2005

easy

1/2

–1/2

1

–1

Q5. The vector sum of two forces is perpendicular to their vector differences. In that case, the forces Source: orcusprep.in

AIPMT 2003

medium

are equal to each other

are equal to each other in magnitude

are not equal to each other in magnitude

cannot be predicted.

Q6. The position vector of a particle is $\mathbf{\vec{r} = (a \cos (\omega t)) \hat{i} + (a \sin (\omega t)) \hat{j}}$. The velocity of the particle is Source: orcusprep.in

AIPMT 1995

medium

directed towards the origin

directed away from the origin

parallel to the position vector

perpendicular to the position vector.

Q7. The angle between the two vectors $\mathbf{\vec{A} = 3\hat{i} + 4\hat{j} + 5\hat{k}}$ and $\mathbf{\vec{B} = 3\hat{i} + 4\hat{j} - 5\hat{k}}$ will be Source: orcusprep.in

AIPMT 1994

easy

90°

180°

zero

45°

Q8. Consider a drop of rain water having mass $1\ \text{g}$ falling from a height of $1\ \text{km}$. It hits the ground with a speed of $50\ \text{m s}^{-1}$. Take $g$ constant with a value $10\ \text{m s}^{-2}$. The work done by the (i) gravitational force and the (ii) resistive force of air is Source: orcusprep.in

NEET 2017

medium

(i) $1.25\ \text{J}$ (ii) $-8.25\ \text{J}$

(i) $100\ \text{J}$ (ii) $8.75\ \text{J}$

(i) $10\ \text{J}$ (ii) $-8.75\ \text{J}$

(i) $-10\ \text{J}$ (ii) $-8.25\ \text{J}$

Q9. A particle of mass $10\ \text{g}$ moves along a circle of radius $6.4\ \text{cm}$ with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to $8 \times 10^{-4}\ \text{J}$ by the end of the second revolution after the beginning of the motion? Source: orcusprep.in

NEET 2016

hard

$0.18\ \text{m/s}^2$

$0.2\ \text{m/s}^2$

$0.1\ \text{m/s}^2$

$0.15\ \text{m/s}^2$

Q10. A bullet of mass $10\ \text{g}$ leaves a rifle at an initial velocity of $1000\ \text{m/s}$ and strikes the earth at the same level with a velocity of $500\ \text{m/s}$. The work done in joule for overcoming the resistance of air will be Source: orcusprep.in

AIPMT 1989

medium

375

3750

5000

500

Q11. A uniform force of $\mathbf{(\hat{3i} + \hat{j})}$ newton acts on a particle of mass $2\ \text{kg}$. Hence the particle is displaced from position $\mathbf{(\hat{2i} + \hat{k})}$ metre to position $\mathbf{(\hat{4i} + \hat{3j} - \hat{k})}$ metre. The work done by the force on the particle is Source: orcusprep.in

NEET 2013

easy

$13\ \text{J}$

$15\ \text{J}$

$9\ \text{J}$

$6\ \text{J}$

Q12. A body moves a distance of $10\ \text{m}$ along a straight line under the action of a $5\ \text{N}$ force. If the work done is $25\ \text{J}$, then angle between the force and direction of motion of the body is Source: orcusprep.in

AIPMT 1997

easy

$60^{\circ}$

$75^{\circ}$

$30^{\circ}$

$45^{\circ}$

Q13. A body, constrained to move in $y$-direction, is subjected to a force given by $\mathbf{\vec{F} = (-2\hat{i} + 15\hat{j} + 6\hat{k})\ \text{N}}$. The work done by this force in moving the body through a distance of $10\hat{j}\ \text{m}$ along $y$-axis, is Source: orcusprep.in

AIPMT 1994

easy

$150\ \text{J}$

$20\ \text{J}$

$190\ \text{J}$

$160\ \text{J}$

Q14. When a body moves with a constant speed along a circle Source: orcusprep.in

AIPMT 1994

no work is done on it

no acceleration is produced in it

its velocity remains constant

no force acts on it.

Q15. A particle of mass $\mathbf{5m}$ at rest suddenly breaks on its own into three fragments. Two fragments of mass $\mathbf{m}$ each move along mutually perpendicular direction with speed $\mathbf{v}$ each. The energy released during the process is Source: orcusprep.in

NEET 2019

hard

$\frac{3}{5} m v^2$

$\frac{5}{3} m v^2$

$\frac{3}{2} m v^2$

$\frac{4}{3} m v^2$

Q16. A body of mass $\mathbf{(4m)}$ is lying in $x-y$ plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass $\mathbf{(m)}$ move perpendicular to each other with equal speeds $\mathbf{(v)}$. The total kinetic energy generated due to explosion is Source: orcusprep.in

NEET 2014

medium

$m v^2$

$\frac{3}{2} m v^2$

$2 m v^2$

$4 m v^2$

Q17. An engine pumps water continuously through a hose. Water leaves the hose with a velocity $\mathbf{v}$ and $\mathbf{m}$ is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water? Source: orcusprep.in

AIPMT 2009

medium

$m v^3$

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

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

$\frac{1}{2} m v^3$

Q18. A shell of mass $\mathbf{200\ \text{gm}}$ is ejected from a gun of mass $\mathbf{4\ \text{kg}}$ by an explosion that generates $\mathbf{1.05\ \text{kJ}}$ of energy. The initial velocity of the shell is Source: orcusprep.in

AIPMT 2008

medium

$40\ \text{m s}^{-1}$

$120\ \text{m s}^{-1}$

$100\ \text{m s}^{-1}$

$80\ \text{m s}^{-1}$

Q19. A bomb of mass $\mathbf{30\ \text{kg}}$ at rest explodes into two pieces of masses $\mathbf{18\ \text{kg}}$ and $\mathbf{12\ \text{kg}}$. The velocity of $\mathbf{18\ \text{kg}}$ mass is $\mathbf{6\ \text{m s}^{-1}}$. The kinetic energy of the other mass is Source: orcusprep.in

AIPMT 2005

medium

$324\ \text{J}$

$486\ \text{J}$

$256\ \text{J}$

$524\ \text{J}$

Q20. A particle of mass $\mathbf{m_1}$ is moving with a velocity $\mathbf{v_1}$ and another particle of mass $\mathbf{m_2}$ is moving with a velocity $\mathbf{v_2}$. Both of them have the same momentum but their different kinetic energies are $\mathbf{E_1}$ and $\mathbf{E_2}$ respectively. If $\mathbf{m_1 > m_2}$ then Source: orcusprep.in

AIPMT 2004

medium

$E_1 < E_2$

$\frac{E_1}{E_2} = \frac{m_1}{m_2}$

$E_1 > E_2$

$E_1 = E_2$

Q21. A ball of mass $\mathbf{2\ \text{kg}}$ and another of mass $\mathbf{4\ \text{kg}}$ are dropped together from a $60\ \text{feet}$ tall building. After a fall of $\mathbf{30\ \text{feet}}$ each towards earth, their respective kinetic energies will be in the ratio of Source: orcusprep.in

AIPMT 2004

easy

$2 : 1$

$1 : 4$

$1 : 2$

Q22. A stationary particle explodes into two particles of masses $\mathbf{m_1}$ and $\mathbf{m_2}$ which move in opposite directions with velocities $\mathbf{v_1}$ and $\mathbf{v_2}$. The ratio of their kinetic energies $\mathbf{E_1/E_2}$ is Source: orcusprep.in

AIPMT 2003

easy

$m_2/m_1$

$m_1/m_2$

$1$

$m_1 v_2 / m_2 v_1$

Q23. If kinetic energy of a body is increased by 300% then percentage change in momentum will be Source: orcusprep.in

AIPMT 2002

medium

$100\%$

$150\%$

$265\%$

$73.2\%$

Q24. A particle is projected making an angle of $\mathbf{45^{\circ}}$ with horizontal having kinetic energy $\mathbf{K}$. The kinetic energy at highest point will be Source: orcusprep.in

AIPMT 2001

medium

$\frac{K}{2}$

$\frac{K}{\sqrt{2}}$

$2K$

$K$

Q25. Two bodies with kinetic energies in the ratio of $\mathbf{4 : 1}$ are moving with equal linear momentum. The ratio of their masses is Source: orcusprep.in

AIPMT 1999

easy

$4 : 1$

$1 : 1$

$1 : 2$

$1 : 4$

Q26. Two bodies of masses $\mathbf{m}$ and $\mathbf{4m}$ are moving with equal kinetic energies. The ratio of their linear momenta is Source: orcusprep.in

AIPMT 1998

easy

$1 : 2$

$1 : 4$

$4 : 1$

$1 : 1$

Q27. The kinetic energy acquired by a mass $\mathbf{m}$ in travelling distance $\mathbf{d}$, starting from rest, under the action of a constant force $\mathbf{F}$ is directly proportional to Source: orcusprep.in

AIPMT 1994

easy

$\sqrt{m}$

$\frac{1}{\sqrt{m}}$

$m$

$\frac{1}{m}$

Q28. Two masses of $\mathbf{1\ \text{g}}$ and $\mathbf{9\ \text{g}}$ are moving with equal kinetic energies. The ratio of the magnitudes of their respective linear momenta is Source: orcusprep.in

AIPMT 1993

easy

$1 : 9$

$9 : 1$

$1 : 3$

$3 : 1$

Q29. A particle of mass $\mathbf{M}$ is moving in a horizontal circle of radius $\mathbf{R}$ with uniform speed $\mathbf{v}$. When it moves from one point to a diametrically opposite point, its Source: orcusprep.in

AIPMT 1992

medium

kinetic energy changes by $M v^2/4$

momentum does not change

momentum changes by $2 M v$

kinetic energy changes by $M v^2$

Q30. A force $\mathbf{F = 20 + 10y}$ acts on a particle in $\mathbf{y}$-direction where $\mathbf{F}$ is in newton and $\mathbf{y}$ in meter. Work done by this force to move the particle from $\mathbf{y = 0}$ to $\mathbf{y = 1\ \text{m}}$ is Source: orcusprep.in

NEET 2019

easy

$20\ \text{J}$

$30\ \text{J}$

$5\ \text{J}$

$25\ \text{J}$

Q31. Force $\mathbf{F}$ on a particle moving in a straight line varies with distance $\mathbf{d}$ as shown in the figure. The work done on the particle during its displacement of $\mathbf{12\ \text{m}}$ is
Source: orcusprep.in

AIPMT 2011

medium

$18\ \text{J}$

$21\ \text{J}$

$26\ \text{J}$

$13\ \text{J}$

Q32. A body of mass $\mathbf{3\ \text{kg}}$ is under a constant force which causes a displacement $\mathbf{s}$ in metres in it, given by the relation $\mathbf{s = \frac{1}{3} t^2}$, where $\mathbf{t}$ is in seconds. Work done by the force in $\mathbf{2\ \text{seconds}}$ is Source: orcusprep.in

AIPMT 2006

medium

$\frac{19}{5}\ \text{J}$

$\frac{5}{19}\ \text{J}$

$\frac{3}{8}\ \text{J}$

$\frac{8}{3}\ \text{J}$

Q33. A force $\mathbf{F}$ acting on an object varies with distance $\mathbf{x}$ as shown here. The force is in $\mathbf{N}$ and $\mathbf{x}$ in $\mathbf{m}$. The work done by the force in moving the object from $\mathbf{x = 0}$ to $\mathbf{x = 6\ \text{m}}$ is
Source: orcusprep.in

AIPMT 2005

easy

$18.0\ \text{J}$

$13.5\ \text{J}$

$9.0\ \text{J}$

$4.5\ \text{J}$

Q34. A force acts on a $\mathbf{3\ \text{g}}$ particle in such a way that the position of the particle as a function of time is given by $\mathbf{x = 3t - 4t^2 + t^3}$, where $\mathbf{x}$ is in metres and $\mathbf{t}$ is in seconds. The work done during the first $\mathbf{4}$ second is Source: orcusprep.in

AIPMT 1998

hard

$490\ \text{mJ}$

$450\ \text{mJ}$

$240\ \text{mJ}$

$530\ \text{mJ}$

Q35. A position dependent force, $\mathbf{F = (7 - 2x + 3x^2) N}$ acts on a small body of mass $\mathbf{2\ \text{kg}}$ and displaces it from $\mathbf{x = 0}$ to $\mathbf{x = 5\ \text{m}}$. The work done in joule is Source: orcusprep.in

AIPMT 1994

medium

$135$

$270$

$35$

$70$

Q36. The potential energy of a particle in a force field is $\mathbf{U(r) = -\frac{A}{r^2} + \frac{B}{r}}$ where $\mathbf{A}$ and $\mathbf{B}$ are positive constants and $\mathbf{r}$ is the distance of the particle from the centre of the field. For stable equilibrium, the distance of the particle is Source: orcusprep.in

AIPMT 2012

medium

$\frac{B}{2A}$

$\frac{2A}{B}$

$\frac{A}{B}$

$\frac{B}{A}$

Q37. The potential energy of a system increases if work is done Source: orcusprep.in

AIPMT 2011

upon the system by a nonconservative force

by the system against a conservative force

by the system against a nonconservative force

upon the system by a conservative force.

Q38. The potential energy between two atoms, in a molecule, is given by $\mathbf{U(x) = \frac{a}{x^{12}} - \frac{b}{x^6}}$ where $\mathbf{a}$ and $\mathbf{b}$ are positive constants and $\mathbf{x}$ is the distance between the atoms. The atom is in stable equilibrium, when Source: orcusprep.in

AIPMT 1995

medium

$\mathbf{x = \left(\frac{2a}{b}\right)^{1/6}}$

$\mathbf{x = \left(\frac{11a}{5b}\right)^{1/6}}$

$\mathbf{x = 0}$

$\mathbf{x = \left(\frac{2a}{b}\right)^{1/6}}$

Q39. A mass $\mathbf{m}$ is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when Source: orcusprep.in

NEET 2019

easy

inclined at an angle of $60^{\circ}$ from vertical

the mass is at the highest point

the wire is horizontal

the mass is at the lowest point

Q40. A body initially at rest and sliding along a frictionless track from a height $\mathbf{h}$ (as shown in the figure) just completes a vertical circle of diameter $\mathbf{AB = D}$. The height $\mathbf{h}$ is equal to
Source: orcusprep.in

NEET 2018

medium

$\frac{3}{2} D$

$D$

$\frac{7}{5} D$

$\frac{5}{4} D$

Q41. What is the minimum velocity with which a body of mass $\mathbf{m}$ must enter a vertical loop of radius $\mathbf{R}$ so that it can complete the loop? Source: orcusprep.in

NEET 2016

easy

$\sqrt{3gR}$

$\sqrt{5gR}$

$\sqrt{gR}$

$\sqrt{2gR}$

Q42. A particle with total energy $\mathbf{E}$ is moving in a potential energy region $\mathbf{U(x)}$. Motion of the particle is restricted to the region when Source: orcusprep.in

NEET 2013

$U(x) < E$

$U(x) = 0$

$U(x) \le E$

$U(x) > E$

Q43. A stone is tied to a string of length $\mathbf{l}$ and is whirled in a vertical circle. At its lowest position, it has a speed $\mathbf{u}$. The magnitude of the **change in velocity** as it reaches a position where the string is horizontal (at height $l$) is Source: orcusprep.in

AIPMT 2003

hard

$\sqrt{2 (u^2 - gl)}$

$\sqrt{u^2 - gl}$

$u - \sqrt{u^2 - 2gl}$

$\sqrt{u^2 + 2gl}$

Q44. A child is sitting on a swing. Its minimum and maximum heights from the ground are $\mathbf{0.75\ \text{m}}$ and $\mathbf{2\ \text{m}}$ respectively, its maximum speed will be ($mathbf{g = 10\ \text{m/s}^2}$) Source: orcusprep.in

AIPMT 2001

easy

$10\ \text{m/s}$

$5\ \text{m/s}$

$8\ \text{m/s}$

$15\ \text{m/s}$

Q45. As shown in the figure, a mass is performing vertical circular motion. The average velocity of the particle is increased, then at which point will the string break? (Points A, B, C, D are typically top, horizontal left, bottom, horizontal right)
Source: orcusprep.in

AIPMT 2000

easy

A (Top)

B (Horizontal)

C (Bottom)

D (Horizontal)

Q46. Two similar springs $\mathbf{P}$ and $\mathbf{Q}$ have spring constants $\mathbf{K_P}$ and $\mathbf{K_Q}$, such that $\mathbf{K_P > K_Q}$. They are stretched first by the same amount (case a), then by the same force (case b). The work done by the springs $\mathbf{W_P}$ and $\mathbf{W_Q}$ are related as, in case (a) and case (b) respectively Source: orcusprep.in

NEET 2015

medium

$W_P > W_Q$ ; $W_Q > W_P$

$W_P < W_Q$ ; $W_Q < W_P$

$W_P = W_Q$ ; $W_P > W_Q$

$W_P = W_Q$ ; $W_P = W_Q$

Q47. A block of mass $\mathbf{M}$ is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant value $\mathbf{k}$. The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be Source: orcusprep.in

AIPMT 2009

medium

$2Mg/k$

$4Mg/k$

$Mg/2k$

$Mg/k$

Q48. A vertical spring with force constant $\mathbf{k}$ is fixed on a table. A ball of mass $\mathbf{m}$ at a height $\mathbf{h}$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $\mathbf{d}$. The **net work done** in the process is Source: orcusprep.in

AIPMT 2007

medium

$mg(h + d) - \frac{1}{2} kd^2$

$mg(h - d) - \frac{1}{2} kd^2$

$mg(h - d) + \frac{1}{2} kd^2$

$mg(h + d) + \frac{1}{2} kd^2$

Q49. The potential energy of a long spring when stretched by $\mathbf{2\ \text{cm}}$ is $\mathbf{U}$. If the spring is stretched by $\mathbf{8\ \text{cm}}$ the potential energy stored in it is Source: orcusprep.in

AIPMT 2006

easy

$U/4$

$4U$

$8U$

$16U$

Q50. A mass of $\mathbf{0.5\ \text{kg}}$ moving with a speed of $\mathbf{1.5\ \text{m/s}}$ on a horizontal smooth surface, collides with a nearly weightless spring of force constant $\mathbf{k = 50\ \text{N/m}}$. The maximum compression of the spring would be Source: orcusprep.in

AIPMT 2004

medium

$0.15\ \text{m}$

$0.12\ \text{m}$

$1.5\ \text{m}$

$0.5\ \text{m}$

Q51. When a long spring is stretched by $\mathbf{2\ \text{cm}}$, its potential energy is $\mathbf{U}$. If the spring is stretched by $\mathbf{10\ \text{cm}}$, the potential energy stored in it will be Source: orcusprep.in

AIPMT 2003

easy

$U/5$

$5U$

$10U$

$25U$

Q52. Two springs $\mathbf{A}$ and $\mathbf{B}$ having spring constant $\mathbf{K_A}$ and $\mathbf{K_B}$ ($mathbf{K_A = 2K_B}$) are stretched by applying **force of equal magnitude**. If energy stored in spring $\mathbf{A}$ is $\mathbf{E_A}$ then energy stored in $\mathbf{B}$ will be Source: orcusprep.in

AIPMT 2001

medium

$2E_A$

$E_A/4$

$E_A/2$

$4E_A$

Q53. A body of mass $\mathbf{1\ \text{kg}}$ is thrown upwards with a velocity $\mathbf{20\ \text{m/s}}$. It momentarily comes to rest after attaining a height of $\mathbf{18\ \text{m}}$. How much energy is lost due to air friction? ($\mathbf{g = 10\ \text{m/s}^2}$) Source: orcusprep.in

AIPMT 2009

medium

$30\ \text{J}$

$40\ \text{J}$

$10\ \text{J}$

$20\ \text{J}$

Q54. $\mathbf{300\ \text{J}}$ of work is done in sliding a $\mathbf{2\ \text{kg}}$ block up an inclined plane of height $\mathbf{10\ \text{m}}$. Work done against friction is ($\mathbf{g = 10\ \text{m/s}^2}$) Source: orcusprep.in

AIPMT 2006

easy

$1000\ \text{J}$

$200\ \text{J}$

$100\ \text{J}$

zero

Q55. A particle of mass $\mathbf{M}$ is driven by a machine that delivers a **constant power $\mathbf{k}$ watts**. If the particle starts from rest, the **force** on the particle at time $\mathbf{t}$ is proportional to Source: orcusprep.in

NEET 2015

hard

$2 \sqrt{mk} t^{-1/2}$

$\frac{1}{2} \sqrt{mk} t^{-1/2}$

$\sqrt{mk} t^{-1/2}$

$mk t^{-1/2}$

Q56. One coolie takes $\mathbf{1\ \text{minute}}$ to raise a suitcase through a height of $\mathbf{2\ \text{m}}$ but the second coolie takes $\mathbf{30\ \text{s}}$ to raise the same suitcase to the same height. The powers of two coolies are in the ratio Source: orcusprep.in

NEET 2013

easy

$1 : 3$

$2 : 1$

$3 : 1$

$1 : 2$

Q57. A car of mass $\mathbf{m}$ starts from rest and accelerates so that the **instantaneous power** delivered to the car has a **constant magnitude $\mathbf{P_0}$**. The instantaneous **velocity** of this car is proportional to Source: orcusprep.in

NEET 2012

medium

$t^2 P_0$

$t^{1/2}$

$t^{-1/2}$

$\frac{t}{m}$

Q58. A body projected vertically from the earth reaches a height equal to earth's radius before returning to the earth. The power exerted by the **gravitational force is greatest** Source: orcusprep.in

AIPMT 2011

medium

at the highest position of the body

at the instant just before the body hits the earth

it remains constant all through

at the instant just after the body is projected

Q59. An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of $\mathbf{2\ \text{m/s}}$. The mass per unit length of water in the pipe is $\mathbf{100\ \text{kg/m}}$. What is the **power** of the engine? Source: orcusprep.in

AIPMT 2010

medium

$400\ \text{W}$

$200\ \text{W}$

$100\ \text{W}$

$800\ \text{W}$

Q60. A particle of mass $\mathbf{M}$, starting from rest, undergoes **uniform acceleration**. If the speed acquired in time $\mathbf{T}$ is $\mathbf{V}$, the **power** delivered to the particle is Source: orcusprep.in

NEET 2010

medium

$\frac{M V^2}{T}$

$\frac{1}{2} \frac{M V^2}{T^2}$

$\frac{M V^2}{T^2}$

$\frac{1}{2} \frac{M V^2}{T}$

Q61. Water falls from a height of $\mathbf{60\ \text{m}}$ at the rate of $\mathbf{15\ \text{kg/s}}$ to operate a turbine. The losses due to frictional forces are $\mathbf{10\%}$ of energy. How much **power is generated** by the turbine ? ($\mathbf{g = 10\ \text{m/s}^2}$) Source: orcusprep.in

AIPMT 2008

medium

$12.3\ \text{kW}$

$7.0\ \text{kW}$

$8.1\ \text{kW}$

$10.2\ \text{kW}$

Q62. If $\mathbf{\vec{F} = (60 \hat{i} + 15\hat{j} - 3\hat{k})\ \text{N}}$ and $\mathbf{\vec{v} = (2 \hat{i} - 4\hat{j} + 5\hat{k})\ \text{m/s}}$, then **instantaneous power** is Source: orcusprep.in

AIPMT 2000

easy

$195\ \text{watt}$

$45\ \text{watt}$

$75\ \text{watt}$

$100\ \text{watt}$

Q63. How much water a pump of $\mathbf{2\ \text{kW}}$ can raise in $\mathbf{one\ \text{minute}}$ to a height of $\mathbf{10\ \text{m}}$ ? (take $\mathbf{g = 10\ \text{m/s}^2}$) Source: orcusprep.in

AIPMT 1990

easy

$1000\ \text{litres}$

$1200\ \text{litres}$

$100\ \text{litres}$

$2000\ \text{litres}$

Q64. Body $\mathbf{A}$ of mass $\mathbf{4m}$ moving with speed $\mathbf{u}$ collides **head on and elastic** with another body $\mathbf{B}$ of mass $\mathbf{2m}$, at rest. After the collision the **fraction of energy lost by the colliding body $\mathbf{A}$** is Source: orcusprep.in

NEET 2019

medium

$5/9$

$1/9$

$8/9$

$4/9$

Q65. A moving block having mass $\mathbf{m}$, collides with another stationary block having mass $\mathbf{4m}$. The **lighter block comes to rest after collision**. When the initial velocity of the lighter block is $\mathbf{v}$, then the value of **coefficient of restitution $\mathbf{(e)}$** will be Source: orcusprep.in

NEET 2018

medium

$0.5$

$0.25$

$0.8$

$0.4$

Q66. A bullet of mass $\mathbf{10\ \text{g}}$ moving horizontally with a velocity of $\mathbf{400\ \text{m s}^{-1}} $ strikes a wooden block of mass $\mathbf{2\ \text{kg}}$ which is suspended by light inextensible string of length $\mathbf{5\ \text{m}}$. As a result, the centre of gravity of the block is found to rise a vertical distance of $\mathbf{10\ \text{cm}}$. The **speed of the bullet after it emerges out** horizontally from the block will be ($ mathbf{g = 10\ \text{m/s}^2}$) Source: orcusprep.in

NEET 2016

hard

$100\ \text{m s}^{-1}$

$80\ \text{m s}^{-1}$

$120\ \text{m s}^{-1}$

$160\ \text{m s}^{-1}$

Q67. Two **identical balls A and B** having velocities of $\mathbf{0.5\ \text{m s}^{-1}}$ and $\mathbf{-0.3\ \text{m s}^{-1}}$ respectively collide **elastically** in one dimension. The velocities of $\mathbf{B}$ and $\mathbf{A}$ after the collision respectively will be Source: orcusprep.in

NEET 2016

easy

$-0.5\ \text{m s}^{-1}$ and $0.3\ \text{m s}^{-1}$

$0.5\ \text{m s}^{-1}$ and $-0.3\ \text{m s}^{-1}$

$-0.3\ \text{m s}^{-1}$ and $0.5\ \text{m s}^{-1}$

$0.3\ \text{m s}^{-1}$ and $0.5\ \text{m s}^{-1}$

Q68. Two particles $\mathbf{A}$ and $\mathbf{B}$, move with constant velocities $\mathbf{\vec{v}_1}$ and $\mathbf{\vec{v}_2}$. At the initial moment their position vectors are $\mathbf{\vec{r}_1}$ and $\mathbf{\vec{r}_2}$ respectively. The condition for particles $\mathbf{A}$ and $\mathbf{B}$ for their **collision** is Source: orcusprep.in

AIPMT 2015

medium

$\vec{r}_1 \times \vec{v}_1 = \vec{r}_2 \times \vec{v}_2$

$\vec{r}_1 - \vec{r}_2 = \vec{v}_1 - \vec{v}_2$

$\frac{\vec{r}_1 - \vec{r}_2}{|\vec{r}_1 - \vec{r}_2|} = \frac{\vec{v}_2 - \vec{v}_1}{|\vec{v}_2 - \vec{v}_1|}$

$\vec{r}_1 \cdot \vec{v}_1 = \vec{r}_2 \cdot \vec{v}_2$

Q69. A ball is thrown vertically downwards from a height of $\mathbf{20\ \text{m}}$ with an initial velocity $\mathbf{v_0}$. It collides with the ground, **loses $\mathbf{50\ \text{percent}}$ of its energy** in collision and **rebounds to the same height**. The initial velocity $\mathbf{v_0}$ is (Take $\mathbf{g = 10\ \text{m s}^{-2}}$) Source: orcusprep.in

AIPMT 2015

hard

$28\ \text{m s}^{-1}$

$10\ \text{m s}^{-1}$

$14\ \text{m s}^{-1}$

$20\ \text{m s}^{-1}$

Q70. On a frictionless surface, a block of mass $\mathbf{M}$ moving at speed $\mathbf{v}$ collides **elastically** with another block of **same mass $\mathbf{M}$** which is initially at rest. After collision the first block moves at an angle $\mathbf{\theta}$ to its initial direction and has a speed $\mathbf{v/3}$. The second block's speed after the collision is Source: orcusprep.in

AIPMT 2015

medium

$\frac{\sqrt{3}}{2} v$

$\frac{3}{2} v$

$\frac{2\sqrt{2}}{3} v$

$\frac{3}{4} v$

Q71. Two particles of masses $\mathbf{m_1, m_2}$ move with initial velocities $\mathbf{u_1}$ and $\mathbf{u_2}$. On collision, one of the particles get excited to higher level, after absorbing energy $\mathbf{\epsilon}$. If final velocities of particles be $\mathbf{v_1}$ and $\mathbf{v_2}$ then we must have Source: orcusprep.in

AIPMT 2015

medium

$\frac{1}{2} m_1 u_1^2 + \frac{1}{2} m_2 u_2^2 - \epsilon = \frac{1}{2} m_1 v_1^2 + \frac{1}{2} m_2 v_2^2$

$\frac{1}{2} m_1 u_1^2 + \frac{1}{2} m_2 u_2^2 + \epsilon = \frac{1}{2} m_1 v_1^2 + \frac{1}{2} m_2 v_2^2$

$m_1 u_1^2 + m_2 u_2^2 - \epsilon = m_1 v_1^2 + m_2 v_2^2$

$\frac{1}{2} m_1 u_1^2 + \frac{1}{2} m_2 u_2^2 = \frac{1}{2} m_1 v_1^2 + \frac{1}{2} m_2 v_2^2 - \epsilon$

Q72. Two spheres $\mathbf{A}$ and $\mathbf{B}$ of masses $\mathbf{m_1}$ and $\mathbf{m_2}$ respectively collide. $\mathbf{A}$ is at rest initially ($u_A=0$) and $\mathbf{B}$ is moving with velocity $\mathbf{v}$ along $\mathbf{x}$-axis ($u_B = v\hat{i}$). After collision $\mathbf{B}$ has a velocity $\mathbf{v/2}$ in a direction **perpendicular to the original direction** ($v_B = \frac{v}{2}\hat{j}$). The mass $\mathbf{A}$ moves after collision in the direction Source: orcusprep.in

AIPMT 2012

hard

same as that of B

opposite to that of B

$\theta = \tan^{-1} \left(\frac{1}{2}\right)$ to the $-x$ axis

$\theta = \tan^{-1} \left(-\frac{1}{2}\right)$ to the $-x$ axis

Q73. A mass $\mathbf{m}$ moving horizontally (along the $x$-axis) with velocity $\mathbf{v}$ collides and **sticks to** a mass of $\mathbf{3m}$ moving vertically upward (along the $y$-axis) with velocity $\mathbf{2v}$. The **final velocity of the combination** is Source: orcusprep.in

NEET 2011

medium

$\frac{3}{2} v \hat{i} + \frac{1}{4} v \hat{j}$

$\frac{1}{4} v \hat{i} + \frac{3}{2} v \hat{j}$

$\frac{1}{3} v \hat{i} + \frac{2}{3} v \hat{j}$

$\frac{2}{3} v \hat{i} + \frac{1}{3} v \hat{j}$

Q74. A ball moving with velocity $\mathbf{2\ \text{m/s}}$ collides **head on** with another stationary ball of **double the mass**. If the **coefficient of restitution is $\mathbf{0.5}$**, then their velocities (in $\mathbf{m/s}$) after collision will be Source: orcusprep.in

AIPMT 2010

hard

$0, 1$

$1, 1$

$1, 0.5$

$0, 2$

Q75. Two **equal masses $\mathbf{m_1}$ and $\mathbf{m_2}$** moving along the same straight line with velocities $\mathbf{+ 3\ \text{m/s}}$ and $\mathbf{-5\ \text{m/s}}$ respectively collide **elastically**. Their velocities after the collision will be respectively Source: orcusprep.in

AIPMT 1998

easy

$-4\ \text{m/s}$ and $+4\ \text{m/s}$

$+4\ \text{m/s}$ for both

$-3\ \text{m/s}$ and $+5\ \text{m/s}$

$-5\ \text{m/s}$ and $+3\ \text{m/s}$

Q76. A rubber ball is dropped from a height of $\mathbf{5\ \text{m}}$ on a plane. On bouncing it rises to $\mathbf{1.8\ \text{m}}$. The ball **loses its velocity on bouncing by a factor of** Source: orcusprep.in

AIPMT 1998

medium

$\frac{3}{5}$

$\frac{2}{5}$

$\frac{16}{25}$

$\frac{9}{25}$

Q77. A metal ball of mass $\mathbf{2\ \text{kg}}$ moving with speed of $\mathbf{36\ \text{km/h}}$ has a **head on collision** with a stationary ball of mass $\mathbf{3\ \text{kg}}$. If after collision, both the balls move as a **single mass**, then the **loss in K.E.** due to collision is Source: orcusprep.in

AIPMT 1997

medium

$100\ \text{J}$

$140\ \text{J}$

$40\ \text{J}$

$60\ \text{J}$

Q78. A moving body of mass $\mathbf{m}$ and velocity $\mathbf{3\ \text{km/hour}}$ collides with a body at rest of mass $\mathbf{2m}$ and **sticks to it**. Now the combined mass starts to move. What will be the **combined velocity**? Source: orcusprep.in

AIPMT 1996

easy

$3\ \text{km/hour}$

$4\ \text{km/hour}$

$1\ \text{km/hour}$

$2\ \text{km/hour}$

Q79. The coefficient of restitution $\mathbf{e}$ for a **perfectly elastic collision** is Source: orcusprep.in

AIPMT 1988

$1$

$0$

$\infty$

$-1$

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Physics - Work Power & Energy-PYQ

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Physics - Work Power & Energy-PYQ

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