The string of a pendulum of length $l$ is displaced through $90^{\circ}$ from the vertical and released. The minimum strength of the string required to withstand the tension as the pendulum passes through the mean position is:

$A$ particle of mass $100 \ g$ is performing vertical circular motion as shown in the figure. Find the tangential acceleration at the given position in $m/s^2$. (Take $g = 10 \ m/s^2$)

For a particle moving in a vertical circle,the total energy at different positions along the path (the motion is under gravity) is:

$A$ block of mass $m$ at the end of a string is whirled round in a vertical circle of radius $R$. The critical speed of the block at the top of its swing below which the string would slacken before the block reaches the top is

$A$ mass $m$ is attached to a string and revolves in a vertical circle. What is the tension in the string when the mass is at the lowest position?

$A$ light rigid wire of length $1 \,m$ is attached to a ball of mass $500 \,g$ at one end. The other end of the wire is fixed, so that the wire can rotate freely in the vertical plane about its fixed end. At the lowest point of the circular motion, the ball is given a horizontal velocity of $6 \,m/s$. Determine the radial component of the acceleration of the ball when this rigid wire makes an angle of $60^{\circ}$ with the upward vertical. (Take $g = 10 \,m/s^2$) (in $\,m/s^2$)