What is the torque of force $\vec F = 2\hat i - 3\hat j + 4\hat k$ acting at a point $\vec r = 3\hat i + 2\hat j + 3\hat k$ about the origin?

Which vector in the figures best represents the acceleration of a pendulum mass at the intermediate point in its swing?

In the $HCl$ molecule, the separation between the nuclei of the two atoms is about $1.27\,\mathop A\limits^o \left( {1\,\mathop A\limits^o  = {{10}^{ - 10}}\,m} \right)$. The approximate location of the centre of mass of the molecule from hydrogen atom, assuming the chlorine atom to be about $35.5$ times massive as hydrogen is ....... $\mathop A\limits^o $

Two rings of the same radius and mass are placed such that their centres are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to the plane of one of the rings is : (mass of the ring $= m,$ radius $= r$ )

The plank in the figure moves a distance $100\,mm$ to the right while the centre of mass of the sphere of radius $150\, mm$ moves a distance $75\,mm$ to the left. The angular displacement of the sphere (in radian) is  (there is no slipping anywhere) :-

A rigid body rotates about a fixed axis with variable angular velocity equal to $(\alpha \,-\,\beta t)$ at time $t,$ where $\alpha $ and $\beta $ are constants. The angle through which it rotates before it comes to rest is