$A$ ball is moving to and fro about the lowest point $A$ of a smooth hemispherical bowl. If it is able to rise up to a height of $20 \,cm$ on either side of $A$,its speed at $A$ must be .......... $m/s$ (Take $g = 10 \,m/s^2$,mass of the body = $5 \,g$).

When an object is released,its potential energy $U$ decreases,and its velocity becomes $v$. What is the mass of the object?

$A$ pendulum bob has a speed $4 \,m/s$ at its lowest position. The pendulum is $1 \,m$ long. When the length of the string makes an angle of $60^{\circ}$ with the vertical, the speed of the bob at that position is (acceleration due to gravity, $g=10 \,m/s^2, \cos 60^{\circ}=0.5$).

$A$ uniform chain of mass $M$ and length $L$ is released from rest from a smooth horizontal surface as shown in the figure. The velocity of the chain at the instant it completely comes off the table will be:

$A$ uniform flexible chain of mass $m$ and length $2l$ hangs in equilibrium over a smooth horizontal pin of negligible diameter. One end of the chain is given a small vertical displacement so that the chain slips over the pin. The speed of the chain when it leaves the pin is

The adjoining diagram shows the velocity versus time plot for a particle. The work done by the force on the particle is positive from