Exercise - 1

A stone of mass of $16 \mathrm{kg}$ is attached to a string $144 \mathrm{m}$ long and is whirled in a horizontal smooth surface. The maximum tension the string can withstand is $16 \mathrm{N}$. The maximum speed of revolution of the stone without breaking it will be,

A particle is kept fixed on a uniformly rotating turn-table. As seen from the ground, the particle goes in a circle, its speed is $10 \mathrm{cm} {\mathrm{s}}^{-1}$ and acceleration is $10 \mathrm{cm} {\mathrm{s}}^{-2}$. The particle is now shifted to a new position to make the radius half of the original value. The new values of the speed and acceleration will be:

A particle moving along a circular path due to a centripetal force having constant magnitude is an example of motion with,

A stone is projected with speed $u$ and angle of projection is $\theta$. Find the radius of curvature at $t = 0$.

A stone tied to a string is rotated in a vertical plane. If the mass of the stone is $m$, the length of the string is $r$ and the linear speed of the stone is $v$ when the stone is at its lowest point, then the tension in the string at the lowest point will be: (Acceleration due to gravity is $g$)

A train $A$ runs from east to west and another train $B$ of the same mass runs from west to east at the same speed with respect to earth along the equator. Normal force by the track on a train $A$ is $N_1$ and that on train $B$ is $N_2$:

If the apparent weight of the bodies at the equator is to be zero, then the earth should rotate with angular velocity (here, $g$ is acceleration due to gravity and $R$ is radius of earth),

A fan is running at $3000 \mathrm{rpm}.$ It is switched off. It comes to rest by uniformly decreasing its angular speed in $10 \mathrm{seconds}.$ The total number of revolutions in this period.