What is the moment of inhertia of a solid sphere of radius $R$ and density $\rho $ about its diameter ?
$\frac{8}{3}\,\pi {R^3}\rho $
$\frac{8}{15}\,\pi {R^5}\rho $
$\frac{8}{3}\,\pi {R^5}\rho $
$\frac{15}{8}\,\pi {R^3}\rho ^2$
Two spheres are rolling with same velocity (for their $C. M.$) their ratio of kinetic energy is $2 : 1$ & radius ratio is $2 : 1$, their mass ratio will be :
A uniform cube of side $a$ and mass $m$ rests on a rough horizontal table. A horizontal force $F$ is applied normal to one of the faces at a point that is directly above the centre of face, at a height $\frac {3a}{4}$ above the base. The minimum value of $F$ for which the cube begins to tilt about the edge is (Assume that the cube does not slide)
A thin circular ring of mass $M$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega $. Two objects, each of mass $m$, are attached gently to the opposite ends of a diameter of the ring. The ring rotates now with an angular velocity
Which vector in the figures best represents the acceleration of a pendulum mass at the intermediate point in its swing?
A ball is thrown on a lawn in such a way that it initially slides with a speed $v_0$ without rolling. It gradually picks up rotation motion. Find the speed of the ball at which there will be rolling without slipping-