$A$ ball falls freely from rest on to a hard horizontal floor and repeatedly bounces. If the velocity of the ball just before the first bounce is $7 \text{ m/s}$ and the coefficient of restitution is $0.75$. The total distance travelled by the ball before it comes to rest is (acceleration due to gravity $= 10 \text{ m/s}^2$) (in $\text{ m}$)

$A$ body of mass $1\,kg$ is thrown upwards with a velocity $20\,m/s$. It momentarily comes to rest after attaining a height of $18\,m$. How much energy is lost due to air friction? (Given $g = 10\,m/s^2$)

$A$ section of a fixed smooth circular track of radius $R$ in a vertical plane is shown in the figure. $A$ block is released from position $A$ and leaves the track at $B$. The radius of curvature of its trajectory when it just leaves the track at $B$ 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 initially at rest. Both the strings are massless and inextensible. If the second bob,after collision,acquires the minimum speed required to complete a full circle in the vertical plane,the ratio $\frac{l_1}{l_2}$ is

Two blocks of masses $m_1$ and $m_2$ are connected by a spring of spring constant $k$,initially at their natural length as shown. $A$ sharp impulse is given to mass $m_2$ so that it acquires a velocity $v_0$ towards the right. If the system is kept on a smooth floor,find the maximum elongation that the spring will suffer.

Two solid rubber balls $A$ and $B$ have masses $200 \ g$ and $400 \ g$ respectively. They are moving towards each other,with ball $A$ having a velocity of $0.3 \ m/s$. After the collision,both balls come to rest. What is the velocity of ball $B$ in $m/s$?