Two particles of masses $2$ g and $4$ g are situated at the opposite ends, A and B of a wooden bar respectively. Let $l(AB) = 9$ cm. The center of mass of the system will be

A force of $3\hat{i} + 2\hat{j} - \hat{k}$ N acts on a particle with position vector $\hat{i} + \hat{j} - \hat{k}$ m. The magnitude of torque of given force is

A satellite is revolving around a planet in a circular orbit close to its surface. Let $\rho$ be mean density and $R$ be the radius of the planet; then the period of the satellite is
($G$ = Universal constant of gravitation).

A metal wire of length 'L' and density 'd' floats horizontally on the free surface of water. The maximum radius of the wire does not sink in water is
[ $T$ = surface tension of water , $g$ = gravitational acceleration]