$A$ man of mass $60 \ kg$ gets $10^5 \ calories$ of energy from food. If his efficiency is $28\%$,up to what height in $m$ can he climb?

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:

Which of the following is generally true when two particles collide?

$A$ $0.5 \, kg$ block moving at a speed of $12 \, ms^{-1}$ compresses a spring through a distance of $30 \, cm$ when its speed is halved. The spring constant of the spring in $N m^{-1}$ is:

Two identical balls of mass $2 \ kg$ are moving towards each other with a velocity of $5 \ m/s$. They collide and come to rest after the collision. What is the work done by the internal forces in $J$?

$A$ sphere of mass $m$ slides down a smooth inclined plane from a point $B$ at a height of $h$ starting from rest. The magnitude of the change in momentum of the particle between position $A$ (at the bottom of the incline) and $C$ (on the horizontal surface) is (assuming the angle of inclination of the plane is $\theta$ with respect to the horizontal):