$A$ body of mass $5 \,kg$ falls from a height of $30 \,m$. If all its mechanical energy is converted into heat,then the heat produced will be ........ $cal$.

Identify the type of collision for the following cases:
$(a)$ Collision between a negatively charged object and a positively charged object.
$(b)$ Collision between two very large objects.
$(c)$ Collision between two quartz balls.

From a building, two balls $A$ and $B$ are thrown such that $A$ is thrown upwards and $B$ is thrown downwards (both vertically) with the same speed. If $v_A$ and $v_B$ are their respective velocities on reaching the ground, then:

$A$ ball falls freely from a height of $180 \,m$ onto a hard horizontal floor and repeatedly bounces. If the coefficient of restitution is $0.5$, the average speed and average velocity of the ball before it ceases to rebound are respectively (acceleration due to gravity $= 10 \,ms^{-2}$)

$A$ spring-block system is resting on a frictionless floor as shown in the figure. The spring constant is $2.0 \,N \,m^{-1}$ and the mass of the block is $2.0 \,kg$. Ignore the mass of the spring. Initially, the spring is in an unstretched condition. Another block of mass $1.0 \,kg$ moving with a speed of $2.0 \,m \,s^{-1}$ collides elastically with the first block. The collision is such that the $2.0 \,kg$ block does not hit the wall. The distance, in metres, between the two blocks when the spring returns to its unstretched position for the first time after the collision is. . . .

$A$ bomb is kept stationary at a point. It suddenly explodes into two fragments of masses $1\,g$ and $3\,g$. The total kinetic energy ($K$.$E$.) of the fragments is $6.4 \times 10^4\,J$. What is the $K$.$E$. of the smaller fragment?