A ball of mass $m,$ at one end of a string of length $L,$ rotates in a vertical circle just fast enough to prevent the string from going slack at the top of the circle. The speed of the ball at the bottom of the circle is

When a block of mass $\text{'}m\text{'}$ is released from point $\text{'}A\text{'}$ on the surface of a smooth bowl, the normal reaction force on it at the lowest point would be equal to

A block of mass $m$ slides down on a smooth parabolic surface from height $h$ as shown. Find its speed at lowermost position

A block of mass $m$ is released from a height $R$ on the frictionless incline as shown. The incline leads to a circle of radius $\frac{R}{2}.$ The maximum height attained by the block is

In the spring mass system shown in the figure, the spring is compressed by $x_0=\frac{mg}{3k}$ from its natural length and the block is released from rest. The speed of the block, when it passes through the point $P$ at means position, is