$A$ car is moving with velocity $v$ at the top of a semi-circular hill of radius $40 \,m$ such that the normal force on it is zero. Find the velocity $(v)$ of the car. [Use $g=10 \,ms^{-2}$] (in $\,ms^{-1}$)

If the string of a conical pendulum makes an angle $\theta$ with the horizontal,then the square of its time period is proportional to

An object of mass $m$ moves with constant speed in a circular path of radius $R$ under the action of a force of constant magnitude $F$. The kinetic energy of the object is ............

Two particles of the same mass are moving in circular orbits because of a force given by $F(r) = -\frac{16}{r} - r^3$. The first particle is at a distance $r = 1$,and the second is at $r = 4$. The best estimate for the ratio of kinetic energies of the first and the second particle is closest to:

$A$ train is moving with a speed of $12 \,m/s$ on rails which are $1.5 \,m$ apart. To negotiate a curve of radius $400 \,m$, the height by which the outer rail should be raised with respect to the inner rail is (Given, $g = 10 \,m/s^2$): (in $\,cm$)

$A$ car is moving with high velocity when it takes a turn. $A$ force acts on it outwardly because of