Core Syllabus Module

Work, Energy, and Power

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Generate random timed arrays filtered strictly by Work, Energy, and Power weightage mappings.

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JEE Advanced (1999)

LEVELJEE Advanced

A particle is suspended vertically from a point $O$ by an inextensible massless string of length $L$ . A vertical line $A B$ is at a distance $L /8$ from $O$ as shown in figure. The object is given a horizontal velocity $u$ . At some point, its motion ceases to be circular and eventually the object passes through the line $A B$ . At the instant of crossing $A B$ , its velocity is horizontal. Find $u$ .

JEE Advanced 1988

LEVELJEE Advanced

A bullet of mass $M$ is fired with a velocity $50 m/s$ at an angle $θ$ with the horizontal. At the highest point of its trajectory, it collides head-on with a bob of mass $3 M$ suspended by a massless string of length $10/3 m$ and gets embedded in the bob. After the collision, the string moves through an angle of $12 0^{\circ}$ . Find (a) the angle $θ$ , (b) the vertical and horizontal coordinates of the initial position of the bob with respect to the point of firing of the bullet. (Take $g = 10 m/s^{2}$ )

JEE Main 2019, 11 Jan Shift-I

LEVELJEE Advanced

A body of mass $1 kg$ falls freely from a height of $100 m$ on a platform of mass $3 kg$ which is mounted on a spring having spring constant $k = 1.25 \times 1 0^{6} N/m$ . The body sticks to the platform and the spring's maximum compression is found to be $x$ . Given that $g = 10 ms^{- 2}$ , the value of $x$ will be close to

(A)

8 cm

(B)

4 cm

(C)

40 cm

(D)

80 cm

JEE Advanced 1998

LEVELJEE Advanced

A particle of mass $1 0^{- 2} kg$ is moving along the positive X-axis under the influence of a force $F (x) = - \frac{k}{2 x ^{2}}$ where $k = 1 0^{- 2} Nm^{2}$ . At time $t = 0$ , it is at $x = 1.0 m$ and its velocity $v = 0$ . (a) Find its velocity when it reaches $x = 0.5 m$ . (b) Find the time at which it reaches $x = 0.25 m$ .

JEE Advanced 2015

LEVELJEE Advanced

A particle of unit mass is moving along the $x$ -axis under the influence of a force and its total energy is conserved. Four possible forms of the potential energy of the particle are given in Column I ( $a$ and $U_{0}$ are constants). Match the potential energies in Column I to the corresponding statements in Column II

List-I

(P)

U_{1} (x) = \frac{U _{0}}{2} [1 - (\frac{x}{a})^{2}]^{2}

(Q)

U_{2} (x) = \frac{U _{0}}{2} (\frac{x}{a})^{2}

(R)

U_{3} (x) = \frac{U _{0}}{2} (\frac{x}{a})^{2} exp [- (\frac{x}{a})^{2}]

(S)

U_{4} (x) = \frac{U _{0}}{2} [\frac{x}{a} - \frac{1}{3} (\frac{x}{a})^{3}]

List-II

(1)

The force acting on the particle is zero at

x = a

(2)

The force acting on the particle is zero at

x = 0

(3)

The force acting on the particle is zero at

x = - a

(4)

The particle experiences an attractive force towards

x = 0

in the region

∣ x ∣ < a

(5)

The particle with total energy

\frac{U _{0}}{4}

can oscillate about the point

x = - a

JEE Advanced 2002

LEVELJEE Advanced

A spherical ball of mass $m$ is kept at the highest point in the space between two fixed, concentric spheres $A$ and $B$ (see fig.). The smaller sphere $A$ has a radius $R$ and the space between the two spheres has a width $d$ . The ball has a diameter very slightly less than $d$ . All surfaces are frictionless. The ball is given a gentle push (towards the right in the figure). The angle made by the radius vector of the ball with the upward vertical is denoted by $θ$ . (a) Express the total normal reaction force exerted by the spheres on the ball as a function of angle $θ$ . (b) Let $N_{A}$ and $N_{B}$ denote the magnitudes of the normal reaction forces on the ball exerted by the spheres $A$ and $B$ , respectively. Sketch the variations of $N_{A}$ and $N_{B}$ as function of $cos θ$ in the range $0 \leq θ \leq π$ by drawing two separate graphs in your answer book, taking $cos θ$ on the horizontal axis.

JEE Advanced 2014

LEVELJEE Advanced

A wire, which passes through the hole in a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from A to B, the force it applies on the wire is

(A)

Always radially outwards

(B)

Always radially inwards

(C)

Radially outwards initially and radially inwards later.

(D)

Radially inwards initially and radially outwards later.

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-I

LEVELJEE Advanced

A small bob tied at one end of a thin string of length 1m is describing a vertical circle, so that the maximum and minimum tension in the string are in the ratio 5 : 1. The velocity of the bob at the highest position is ……… m/s. (Take, $g = 10 m/s^{2}$ )

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 Advanced

The potential energy of a $1 kg$ particle free to move along the x-axis is given by $V (x) = (\frac{x ^{4}}{4} - \frac{x ^{2}}{2}) J$ The total mechanical energy of the particle is $2 J$ . Then, the maximum speed (in $ms^{- 1}$ ) is

(A)

\frac{3}{2}

(B)

2

(C)

\frac{1}{2}

(D)

2

JEE Main 2021, 27 July Shift-II

LEVELJEE Advanced

A small block slides down from the top of hemisphere of radius $R = 3$ m as shown in the figure. The height $h$ at which the block will lose contact with the surface of the sphere is ………… m. (Assume there is no friction between the block and the hemisphere)

JEE Main 2021, 27 Aug Shift-II

LEVELJEE Advanced

A bullet of $10 g$ , moving with velocity $v$ , collides head-on with the stationary bob of a pendulum and recoils with velocity $100 m/s$ . The length of the pendulum is $0.5 m$ and mass of the bob is $1 kg$ . The minimum value of $v$ .......... $m/s$ , so that the pendulum describes a circle. (Assume, the string to be inextensible and $g = 10 m/s^{2}$ )

JEE Main 2019

LEVELJEE Advanced

A block of mass $m$ lying on a smooth horizontal surface is attached to a spring (of negligible mass) of spring constant $k$ . The other end of the spring is fixed as shown in the figure. The block is initially at rest in its equilibrium position. If now the block is pulled with a constant force $F$ , the maximum speed of the block is

(A)

\frac{π F}{mk}

(B)

\frac{F}{mk}

(C)

\frac{2 F}{mk}

(D)

\frac{F}{π mk}

JEE Main 2016

LEVELJEE Advanced

A point particle of mass $m$ , moves along the uniformly rough track $P QR$ as shown in the figure. The coefficient of friction between the particle and the rough track equals $μ$ . The particle is released, from rest, from the point $P$ and it comes to rest at a point $R$ . The energies, lost by the ball, over the parts, $P Q$ and $QR$ , of the track, are equal to each other, and no energy is lost when particle changes direction from $P Q$ to $QR$ . The values of the coefficient of friction $μ$ and the distance $x (= QR)$ , are respectively close to

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

JEE Advanced 2013

LEVELJEE Advanced

A bob of mass $m$ , suspended by a string of length $l_{1}$ , is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass $m$ suspended by a string of length $l_{2}$ , which is initially at rest. Both the strings are massless and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio $l_{1} / l_{2}$ is

JEE Advanced 2008

LEVELJEE Advanced

A block ( $B$ ) is attached to two unstretched springs $S_{1}$ and $S_{2}$ with spring constants $k$ and $4 k$ , respectively. The other ends are attached to two supports $M_{1}$ and $M_{2}$ not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block $B$ is displaced towards wall 1 by a small distance $x$ and released. The block returns and moves a maximum distance $y$ towards wall 2. Displacements $x$ and $y$ are measured with respect to the equilibrium position of the block $B$ . The ratio $\frac{y}{x}$ is

(A)

(B)

(C)

\frac{1}{2}

(D)

\frac{1}{4}

JEE Advanced (2008)

LEVELJEE Advanced

A bob of mass $M$ is suspended by a massless string of length $L$ . The horizontal velocity $v$ at position $A$ is just sufficient to make it reach the point $B$ . The angle $θ$ at which the speed of the bob is half of that at $A$ , satisfies

(A)

θ = \frac{π}{4}

(B)

\frac{π}{4} < θ < \frac{π}{2}

(C)

\frac{π}{2} < θ < \frac{3 π}{4}

(D)

\frac{3 π}{4} < θ < π

Micro-Topic Strategy Matrix

Work Done by Forces

Kinetic Energy, Potential Energy and Power

Conservation of Mechanical Energy

Vertical Circular Motion

Chapter Elite-20 Challenge Zone

List-I

List-II