Work, Power & Energy — JEE Advanced PYQs

A disk of radius $R$ with uniform positive charge density $\sigma$ is placed on the $xy$ plane with its center at the origin. The Coulomb potential along the $z$-axis is

A particle of positive charg …

A particle is moved along a path AB-BC-CD-DE-EF-FA, as shown in figure, in presence of a force $\overrightarrow{\mathrm{F}}=(\alpha \mathrm{y}\hat{\mathrm{i}}+2\alpha \mathrm{x}\hat{\mathrm{j}})$ N, where x and y are in meter and $\alpha =-1\mathrm{N}/{\mathrm{m}}^{-1}$. The …

A particle of mass $m$ is initially at rest at the origin. It is subjected to a force and starts moving along the $x$-axis. Its kinetic energy $K$ changes with time as $dK/dt=\gamma t$, where $\gamma$ is a positive constant of appropriate dimensions. Which of the foll …

Two identical uniform discs roll without slipping on two different surfaces $AB$ and $CD$ (see figure) starting at $A$ and $C$ with linear speeds $v_1$ and $v_2$, respectively, and always remain in contact with the surfaces. If they reach $B$ and $D$ with the same linear spee …

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 ${\mathrm{U}}_0$ are constants). Match the potential energies in column I …

Consider an elliptically shaped rail PQ in the vertical plane with $\mathrm{OP}=3m$ and $\mathrm{OQ}=4m$. A block of mass 1 kg is pulled along the rail from P to Q with a force of $18N$, which is always parallel to line PQ (see the figure given). Assuming no frictional …

The work done on a particle of mass $m$ by a force, $K\left[\frac{x}{{\left(x^2+y^2\right)}^{3/2}}\hat{i}+\frac{y}{{\left(x^2+y^2\right)}^{3/2}}\hat{j}\right]$ ( $K$ being a constant of appropriate dimensions), when the particle is taken from the point $(a,0)$ …

A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to the particle. If the initial speed (in $m{s}^{-1}$ ) of the particle is zero, the speed (in $m{s}^{-1}$ ) after $5s$ is

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 i …

Paragraph for Questions 13 and 14

A small block of mass $1kg$ is released from rest at the top of a rough track. The track is a circular arc of radius $40m$. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to th …

Paragraph for Questions 13 and 14

A small block of mass $1kg$ is released from rest at the top of a rough track. The track is a circular arc of radius $40m$. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to th …

A block of mass 0.18 kg is attached to a spring of force-constant 2 N/m. The coefficient of friction between the block and the floor is 0.1. Initially the block is at rest and the spring is un-stretched. An impulse is given to the block as shown in the figure. The block slides a …

When a particle of mass m moves on the x-axis in a potential of the form $V(x)=k{x}^2$, it performs simple harmonic motion. The corresponding time period is proportional to $\sqrt{\frac{m}{k}}$, as can be seen easily using dimensional analysis. However, the motion of a particle c …

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 seconds is

A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure. The angle of the incline suddenly changes from $60^{\circ }$ to $30^{\circ }$ at point B . The block is initially at rest at A. Assume that collisions between the block and the inc …

A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure. The angle of the incline suddenly changes from $60^{\circ }$ to $30^{\circ }$ at point B . The block is initially at rest at A. Assume that collisions between the block and the inc …

Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertia $I$ and $2I$ respectively about the common axis. Disc A is imparted an initial angular velocity $2\omega$ using the entire potential energy of a spring compressed by a distance …