$A$ block moving horizontally on a smooth surface with a speed of $40\, m/s$ splits into two parts with masses in the ratio of $1:2$. If the smaller part moves at $60\, m/s$ in the same direction,then the fractional change in kinetic energy is:

$A$ ball is dropped from a height of $20 \, cm$. The ball rebounds to a height of $10 \, cm$. What is the percentage loss of energy? ................ $\%$

Particle $A$ of mass $m_{1}$ moving with velocity $(\sqrt{3} \hat{i} + \hat{j}) \, m/s$ collides with another particle $B$ of mass $m_{2}$ which is at rest initially. Let $\vec{V}_{1}$ and $\vec{V}_{2}$ be the velocities of particles $A$ and $B$ after collision,respectively. If $m_{1} = 2m_{2}$ and after collision $\vec{V}_{1} = (\hat{i} + \sqrt{3} \hat{j}) \, m/s$,the angle between $\vec{V}_{1}$ and $\vec{V}_{2}$ is $......^{\circ}$.

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:

$A$ lorry and a car moving with the same $K.E.$ are brought to rest by applying the same retarding force,then

Two identical balls $A$ and $B$ are released from the positions shown in the figure. They collide elastically on the horizontal portion $MN$. All surfaces are smooth. The ratio of the maximum heights attained by $A$ and $B$ after the collision will be (Neglect energy loss at $M$ and $N$):