$A$ ring of mass $m$ and radius $R$ has three particles attached to the ring as shown in the figure. The centre of the ring has a speed $v_0$. The kinetic energy of the system is: (Slipping is absent)
$6\, mv_0^2$
$12\,mv_0^2$
$12\,mv_0^2$
$8\,mv_0^2$
A student of mass $M$ is $1.5 \,m$ tall and has her centre of mass $1 \,m$ above ground when standing straight. She wants to jump up vertically. To do so. she bends her knees so that her centre of mass is lowered by $0.2 \,m$ and then pushes the ground by a constant force F. As a result, she jumps up such that the maximum height of her feet is $0.3 \,m$ above ground. The ratio $F / Mg$ is
A small object of uniform density rolls up a curved surface with an initial velocity $v$. It reaches upto a maximum height of $3v^2/4g$ with respect to the initial position. The object is
Write the formula for rotational kinetic energy.
The ratio of rotational and translatory kinetic energies of a sphere is
A disc of mass $3 \,kg$ rolls down an inclined plane of height $5 \,m$. The translational kinetic energy of the disc on reaching the bottom of the inclined plane is .......... $J$