$A$ $2 \, kg$ block is placed on a frictionless inclined plane with an angle of $30^\circ$ and a length of $2 \, m$. After reaching the bottom of the incline,it travels on a surface with a coefficient of friction of $0.25$. What distance (in $m$) will it travel on the surface before coming to rest?

$A$ block of mass $m$ starts from rest and slides down a frictionless semi-circular track from a height $h$ as shown. When it reaches the lowest point of the track,it collides with a stationary piece of putty also having mass $m$. If the block and the putty stick together and continue to slide,the maximum height that the block-putty system could reach is:

$A$ ball of mass $0.2 \ kg$ is at rest at a height of $5 \ m$. $A$ bullet of mass $0.01 \ kg$ moving horizontally with a velocity $V \ m/s$ strikes the center of the ball. After the collision,the ball and the bullet move independently. The ball hits the ground at a distance of $20 \ m$ and the bullet hits the ground at a distance of $100 \ m$ from the base of the pillar. What is the initial velocity $V$ of the bullet in $m/s$?

$A$ machine with efficiency $2/3$ uses $12 \text{ J}$ of energy to lift a $2 \text{ kg}$ block to a certain height. If the block is allowed to fall freely from that height,what is its velocity when it reaches the ground?

Three objects $A, B$ and $C$ are kept in a straight line on a frictionless horizontal surface. The masses of $A, B$ and $C$ are $m, 2m$ and $2m$ respectively. $A$ moves towards $B$ with a speed of $9 \ m/s$ and makes an elastic collision with it. Thereafter,$B$ makes a completely inelastic collision with $C$. All motions occur along the same straight line. The final speed of $C$ is $.... \ m/s$.

$A$ ball is released from a certain height. It loses $50\%$ of its kinetic energy on striking the ground. It will attain a height again equal to