A small block of mass $100 \mathrm{g}$ is pressed against a horizontal spring fixed at one end to compress the spring through $5.0 \mathrm{cm}$. The spring constant is $100 \mathrm{N} {\mathrm{m}}^{-1}$ When released, the block moves horizontally till it leaves the spring. Calculate horizontal range in meter, if the ground is $2 \mathrm{m}$ below the spring?

   

A small heavy block is attached to the lower end of a light rod of length $I$ which can be rotated about its clamped upper end. $\sqrt{agl}$ is minimum horizontal velocity should the block be given so that it moves in a complete vertical circle. Find the value of $2a$. 

Figure shows two blocks $A$ and $B$, each having a mass of $320 \mathrm{g}$ connected by a light string passing over a smooth light pulley. The horizontal surface on which the block $A$ can slide is smooth. The block $A$ is attached to a spring of spring constant $40 \mathrm{N}/\mathrm{m}$ whose other end is fixed to a support $40 \mathrm{cm}$ above the horizontal surface. Initially, the spring is vertical and unstretched when the system is released to move. Find the velocity $\left(\mathrm{in} {\mathrm{ms}}^{-1}\right)$ of the block $A$ at the instant it breaks off the surface below it. (Take $g=10 \mathrm{m}/{\mathrm{s}}^2$)

One end of a spring of natural length $h$ and spring constant $k$ is fixed at the ground and the other is fitted with a smooth ring of mass $m$ which is allowed to slide on a horizontal rod fixed at a height $h$, as shown in the figure. Initially, the spring makes an angle of $37°$ with the vertical when the system is released from rest. Find the speed of the ring when the spring becomes vertical.

Shows a light rod of length $l$ rigidly attached to a small heavy block at one end and a hook at the other end. The system is released from rest with the rod in a horizontal position. There is a fixed smooth ring at a depth $h$ below the initial position of the hook and the hook gets into the ring as it reaches there. What should be the minimum value of $h$ so that the block moves in a complete circle about the ring?

The bob of a pendulum at rest is given a sharp hit to impart a horizontal velocity $\sqrt{10gl}$, where $l$ is the length of the pendulum. Find the tension in the string when

(a) the string is horizontal,

(b) the bob is at its highest point and

(c) the string makes an angle of $60°$ with the upward vertical.

A simple pendulum consists of a $50 \mathrm{cm}$ long string connected to a $100 \mathrm{g}$ ball. The ball is pulled aside so that the string makes an angle of $37°$ with the vertical and is then released. Find the tension in the string when the ball is at its lowest position.