Find the torque of a force $\vec F = -3\hat i + \hat j + 5\hat k$ acting at the point $\vec r = 7\hat i + 3\hat j + \hat k$ with respect to origin
$14\hat i - 38\hat j +16\hat k$
$4\hat i + 4\hat j + 6\hat k$
$-14\hat i + 38\hat j - 16\hat k$
$-21\hat i + 3\hat j + 5\hat k$
Radius of gyration of a uniform thin rod of length $L$ about an axis passing normally through its centre of mass is
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
A force $\vec F$ acts on a particle having position vector $\vec r$ (with respect to origin). It produces a torque $\vec \tau $ about origin, choose the correct option
A mass $‘m’$ is supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R$. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?
A cylinder of mass $M$ and radius $r$ is mounted on a frictionless axle over a well. A rope of negligible mass is wrapped around the solid cylinder and a bucket of mass $m$ is suspended from the rope. The linear acceleration of the bucket will be