Kinetic Energy, Potential Energy and Power

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The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U (x) = \frac{a}{x ^{12}} - \frac{b}{x ^{6}}$ , where $a$ and $b$ are constants and $x$ is the distance between the atoms. If the dissociation energy of the molecule is $D = [U (x = \infty) - U_{at equilibrium}]$ , then $D$ is

\frac{b ^{2}}{2 a}

(B)

\frac{b ^{2}}{12 a}

(C)

\frac{b ^{2}}{4 a}

(D)

\frac{b ^{2}}{6 a}

LEVELJEE Main

The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U (x) = \frac{a}{x ^{12}} - \frac{b}{x ^{6}}$ , where $a$ and $b$ are constants and $x$ is the distance between the atoms. If the dissociation energy of the molecule is $D = [U (x = \infty) - U_{at equilibrium}]$ , $D$ is

(A)

\frac{b ^{2}}{2 a}

(B)

\frac{b ^{2}}{12 a}

(C)

\frac{b ^{2}}{4 a}

(D)

\frac{b ^{2}}{6 a}

JEE Main 2021

LEVELJEE Main

The potential energy ( $U$ ) of a diatomic molecule is a function dependent on $r$ (interatomic distance) as $U = \frac{α}{r ^{10}} - \frac{β}{r ^{5}}$ , where $α$ and $β$ are positive constants. The equilibrium distance between two atoms will be $(\frac{2 α}{β})^{\frac{a}{b}}$ , where $a = \dots\dots$ .

JEE Main 2021, 20 July Shift-II

LEVELJEE Main

If the kinetic energy of a moving body becomes four times of its initial kinetic energy, then the percentage change in its momentum will be

An athlete in the olympic games covers a distance of $100$ m in $10$ s. His kinetic energy can be estimated to be in the range

(A)

200

J -

500

(B)

2 \times 1 0^{5}

J -

3 \times 1 0^{5}

(C)

20000

J -

50000

(D)

2000

J -

5000

JEE Main 2021, 24 Feb Shift-II

LEVELJEE Main

Two solids $A$ and $B$ of mass $1 kg$ and $2 kg$ respectively are moving with equal linear momentum. The ratio of their kinetic energies $(KE)_{A} : (KE)_{B}$ will be $\frac{A}{1}$ , so the value of $A$ will be ……… .

JEE Main 2020, 6 Sep Shift-I

LEVELJEE Main

If the potential energy between two molecules is given by $U = - \frac{A}{r ^{6}} + \frac{B}{r ^{12}}$ , then at equilibrium, separation between molecules and the potential energy are

(A)

(\frac{B}{2 A})^{1/6}, - \frac{A ^{2}}{2 B}

(B)

(\frac{B}{A})^{1/6}, 0

(C)

(\frac{2 B}{A})^{1/6}, - \frac{A ^{2}}{4 B}

(D)

(\frac{2 B}{A})^{1/6}, - \frac{A ^{2}}{2 B}

JEE Main 2020, 7 Jan Shift-II

LEVELJEE Main

An elevator in a building can carry a maximum of $10$ persons with the average mass of each person being $68 kg$ . The mass of the elevator itself is $920 kg$ and it moves with a constant speed of $3 m/s$ . The frictional force opposing the motion is $6000 N$ . If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator ( $g = 10 m/s^{2}$ ) must be at least

(A)

62360 W

(B)

48000 W

(C)

56300 W

(D)

66000 W

JEE Main 2021, 17 March Shift-I

LEVELJEE Main

A boy is rolling a $0.5 kg$ ball on the frictionless floor with the speed of $20 ms^{- 1}$ . The ball gets deflected by an obstacle on the way. After deflection it moves with 5% of its initial kinetic energy. What is the speed of the ball now ?

(A)

19.0 ms^{- 1}

(B)

4.47 ms^{- 1}

(C)

14.41 ms^{- 1}

(D)

1.00 ms^{- 1}

JEE Main 2019, 9 April Shift-I

LEVELJEE Main

A uniform cable of mass $M$ and length $L$ is placed on a horizontal surface such that its $(\frac{1}{n})$ th part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be

(A)

\frac{2 M g L}{n ^{2}}

(B)

n M g L

(C)

\frac{M g L}{n ^{2}}

(D)

\frac{M g L}{2 n ^{2}}

JEE Main 2017

LEVELJEE Advanced

A body of mass $m = 1 0^{- 2} kg$ is moving in a medium and experiences a frictional force $F = - k v^{2}$ . Its initial speed is $v_{0} = 10 ms^{- 1}$ . If, after 10 s, its energy is $\frac{1}{8} m v_{0}^{2}$ , the value of $k$ will be

(A)

1 0^{- 3} kgs^{- 1}

(B)

1 0^{- 4} kgm^{- 1}

(C)

1 0^{- 1} kgm^{- 1} s^{- 1}

(D)

1 0^{- 3} kgm^{- 1}

JEE Main 2021 (25 Feb Shift-II)

LEVELJEE Main

Two particles having masses $4 g$ and $16 g$ respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is $n : 2$ . The value of $n$ will be ............ .

JEE Main 2020, 5 Sep Shift-II

LEVELJEE Advanced

A body of mass $2 kg$ is driven by an engine delivering a constant power of $1 J/s$ . The body starts from rest and moves in a straight line. After $9 s$ , the body has moved a distance (in m) ......... .

LEVELJEE Main

A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time $t$ is proportional to

(A)

t^{3/4}

(B)

t^{3/2}

(C)

t^{1/4}

(D)

t^{1/2}

LEVELJEE Main

At time $t = 0$ , particle starts moving along the x-axis. If its kinetic energy increases uniformly with time $t$ , the net force acting on it must be proportional to

(A)

t

(B)

constant

(C)

t

(D)

1/ t

JEE Main 2020

LEVELJEE Main

A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement (s)-time (t) graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale)

JEE Main 2021, 27 July Shift-II

LEVELJEE Main

An automobile of mass $m$ accelerates starting from origin and initially at rest, while the engine supplies constant power $P$ . The position is given as a function of time by

(A)

(\frac{9 P}{8 m})^{\frac{1}{2}} t^{\frac{3}{2}}

(B)

(\frac{8 P}{9 m})^{\frac{1}{2}} t^{\frac{2}{3}}

(C)

(\frac{9 m}{8 P})^{\frac{1}{2}} t^{\frac{3}{2}}

(D)

(\frac{8 P}{9 m})^{\frac{1}{2}} t^{\frac{3}{2}}

JEE Main 2021, 18 March Shift-II

LEVELJEE Main

A particle of mass $m$ moves in a circular orbit under the central potential field, $U (r) = \frac{- C}{r}$ , where $C$ is a positive constant. The correct radius-velocity graph of the particle's motion is

A body of mass $m$ is accelerated uniformly from rest to a speed $v$ in a time $T$ . The instantaneous power delivered to the body as a function of time, is given by

(A)

\frac{m v ^{2}}{T ^{2}} t

(B)

\frac{m v ^{2}}{T ^{2}} t^{2}

(C)

\frac{1}{2} \frac{m v ^{2}}{T ^{2}} t

(D)

\frac{1}{2} \frac{m v ^{2}}{T ^{2}} t^{2}

JEE Main 2020, 7 Jan Shift-I

LEVELJEE Main

A 60 HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to (Take, $1 HP = 746 W, g = 10 ms^{- 2}$ )

(A)

2.0 ms^{- 1}

(B)

1.5 ms^{- 1}

(C)

1.9 ms^{- 1}

(D)

1.7 ms^{- 1}

JEE Main 2018

LEVELJEE Main

A particle is moving in a circular path of radius $a$ under the action of an attractive potential $U = - \frac{k}{2 r ^{2}}$ . Its total energy is

(A)

- \frac{k}{4 a ^{2}}

(B)

\frac{k}{2 a ^{2}}

(C)

zero

(D)

- \frac{3}{2} \frac{k}{a ^{2}}

JEE Main 2021, 20 July Shift-II

LEVELJEE Main

A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time $t$ is proportional to

(A)

t^{3/2}

(B)

t^{1/2}

(C)

t^{1/4}

(D)

t^{3/4}

JEE Main 2021, 18 March Shift-I

LEVELJEE Main

A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time $t$ is proportional to

(A)

t^{2/3}

(B)

t^{3/2}

(C)

t

(D)

t^{1/2}

JEE Advanced (2014)

LEVELJEE Advanced

A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy $K$ with time $t$ most appropriately? The figures are only illustrative and not to the scale.

A block of mass $2 kg$ is free to move along the $x$ -axis. It is at rest and from $t = 0$ onwards it is subjected to a time-dependent force $F (t)$ in the $x$ -direction. The force $F (t)$ varies with $t$ as shown in the figure. The kinetic energy of the block after $4.5 s$ is

(A)

4.50 J

(B)

7.50 J

(C)

5.06 J

(D)

14.06 J

If the kinetic energy of a moving body becomes four times of its initial kinetic energy, then the percentage change in its momentum will be

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the potential energy between two molecules is given by U=−r6A​+r12B​, then at equilibrium, separation between molecules and the potential energy are

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time t is proportional to

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } At time t=0, particle starts moving along the x-axis. If its kinetic energy increases uniformly with time t, the net force acting on it must be proportional to

A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement (s)-time (t) graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale)

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } An automobile of mass m accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A body of mass m is accelerated uniformly from rest to a speed v in a time T. The instantaneous power delivered to the body as a function of time, is given by

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A particle is moving in a circular path of radius a under the action of an attractive potential U=−2r2k​. Its total energy is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time t is proportional to

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time t is proportional to

An athlete in the olympic games covers a distance of $100$ m in $10$ s. His kinetic energy can be estimated to be in the range

If the potential energy between two molecules is given by $U = - \frac{A}{r ^{6}} + \frac{B}{r ^{12}}$ , then at equilibrium, separation between molecules and the potential energy are

A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time $t$ is proportional to

At time $t = 0$ , particle starts moving along the x-axis. If its kinetic energy increases uniformly with time $t$ , the net force acting on it must be proportional to

An automobile of mass $m$ accelerates starting from origin and initially at rest, while the engine supplies constant power $P$ . The position is given as a function of time by

A body of mass $m$ is accelerated uniformly from rest to a speed $v$ in a time $T$ . The instantaneous power delivered to the body as a function of time, is given by

A particle is moving in a circular path of radius $a$ under the action of an attractive potential $U = - \frac{k}{2 r ^{2}}$ . Its total energy is

A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time $t$ is proportional to

A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time $t$ is proportional to