Embibe Experts Solutions for Chapter: Work, Energy and Power, Exercise 1: JEE Main - 1 September 2021 Shift 2

Identify the correct statements from the following:

(A) Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative

(B) Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative

(C) Work done by friction on a body sliding down an inclined plane is positive

(D) Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity is zero

(E) Work done by the air resistance on an oscillating pendulum is negative

Choose the correct answer from the options given below:

As per the given figure, a small ball $P$ slides down the quadrant of a circle and hits the other ball $Q$ of equal mass which is initially at rest. Neglecting the effect of friction and assume the collision to be elastic, the velocity of ball $Q$ after collision will be : $(g = 10 \mathrm{m} {\mathrm{s}}^{-2})$ 

A ball of mass $200 \mathrm{g}$ rests on a vertical post of height $20 \mathrm{m}$. A bullet of mass $10 \mathrm{g}$, travelling in horizontal direction, hits the centre of the ball. After collision both travels independently. The ball hits the ground at a distance $30 \mathrm{m}$ and the bullet at a distance of $120 \mathrm{m}$ from the foot of the post. The value of initial velocity of the bullet will be (if $g=10 \mathrm{m} {\mathrm{s}}^{-2}$) :

A body of mass $2 \mathrm{kg}$ is initially at rest. It starts moving unidirectionally under the influence of a source of constant power $P$. Its displacement in $4 \mathrm{s}$ is $\frac{1}{3}{\alpha }^2\sqrt{P} \mathrm{m}$. The value of $\alpha$ will be ______.

A lift of mass $M=500 \mathrm{kg}$ is descending with speed of $2 \mathrm{m} {\mathrm{s}}^{-1}$. Its supporting cable begins to slip thus allowing it to fall with a constant acceleration of $2 \mathrm{m} {\mathrm{s}}^{-2}$. The kinetic energy of the lift at the end of fall through to a distance of $6 \mathrm{m}$ will be ______ $\mathrm{kJ}$.

A ball is dropped from a height of $20 \mathrm{m}$. If the coefficient of restitution for the collision between ball and floor is $0.5$, after hitting the floor, the ball rebounds to a height of ______ $\mathrm{m}$.

A small particle moves to position $5\hat{i}-2\hat{j}+\hat{k}$ from its initial position $2\hat{i}+3\hat{j}-4\hat{k}$ under the action of force $5\hat{i}+2\hat{j}+7\hat{k} \mathrm{N}$. The value of work done will be ______ $\mathrm{J}$.

A force $F=(5+3y^2)$ acts on a particle in the $y$-direction, where $F$ is newton and $y$ is in meter. The work done by the force during a displacement from $y=2 \mathrm{m}$ to $y=5 \mathrm{m}$ is ______ $\mathrm{J}$.