A body of mass $m$ is moving in a circle of radius $r$ with a constant speed $v$. The work done by the centripetal force in moving the body over half the circumference of the circle is

Two particles $\mathrm{A},\mathrm{ }\mathrm{B}$ are moving on two concentric circles of radii $R_1$ and $R_2$ with equal angular speed $\omega .$ At $t=0,$ their positions and direction of motion are shown in the figure:

The relative velocity $\overrightarrow{V_A}-\overrightarrow{V_B}$ at $t=\frac{\pi }{2\omega }$ is given by:

What is an artificial satellite? Name any two types of artificial satellite and state their functions.

A small block of mass $100 \mathrm{g}$ is tied to a spring of spring constant $7.5 \mathrm{N} {\mathrm{m}}^{-1}$ and length $20 \mathrm{cm}.$ The other end of spring is fixed at a particular point $A.$ If the block moves in a circular path on a smooth horizontal surface with constant angular velocity $5 \mathrm{rad} {\mathrm{s}}^{-1}$about point $A,$ then tension in the spring is

A mass $\text{m}$ moves in a circle on a smooth horizontal plane with velocity ${\mathrm{v}}_0$ at a radius ${\mathrm{R}}_0$ . The mass is attached to a string which passes through a smooth hole in plane as shown.

The tension in the string is increased gradually and finally $\text{m}$ moves in a circle of radius $\frac{{\mathrm{R}}_0}{2}$. The final value of the kinetic energy is:

If the kinetic energy of a particle of mass $m,$ performing uniform circular motion in a circle of radius $r,$ is $E,$ find the acceleration of the particle.

Two stones of masses $m$ and $2m$ are whirled in horizontal circles, the heavier one in radius $\frac{r}{2}$ and the lighter one in radius $r$. The tangential speed of lighter stone is $n$ times that of the tangential speed of the heavier stone. They are reported to experience the same centripetal force. The value of $n$ is,