A body, initially at rest, starts rotating with a uniform acceleration and covers $100\pi \mathrm{rad}$ in the first $5$ seconds. Its angular speed at the end of $5$ seconds is

A particle is moving in a circle and is uniformly gaining speed. Match the following physical quantities:

Two spheres of equal masses are attached to a string of length $2 \mathrm{m}$ as shown in figure. The string and the sphere are then whirled in a horizontal circle about $O$ at a constant rate. What is the value of the ratio?
$\frac{\left(\mathrm{Tension} \mathrm{in} \mathrm{the} \mathrm{string} \mathrm{between} P \mathrm{and} Q\right)}{\left(\mathrm{Tension} \mathrm{in} \mathrm{the} \mathrm{string} \mathrm{between} P \mathrm{and} O\right)}=$?

The Earth (of mass $6\times {10}^{24} \mathrm{kg}$ ) revolves round the sun with an angular velocity of $2\times {10}^{-7} \mathrm{rad} {\mathrm{s}}^{-1}$ in a circular orbit of radius $1.5\times {10}^{11} \mathrm{km}.$ The force exerted by the sun on the earth is $\underline{ }$