The force $7\hat i + 3\hat j - 5\hat k$ acts on a particle whose position vector is $\hat i - \hat j + \hat k$. What is the torque of a given force about the origin ?

We have two spheres one of which is hollow and the other solid. They have identical masses and moment of inertia about their respectively diameters. The ratio of their radius is given by

Two discs of moments of inertia $I_1$ and $I_2$ about their respective axes (normal to the disc and passing through the centre), and rotating with angular speed $\omega _1$ and $\omega _2$ are brought into contact face to face with their axes of rotation coincident. What is the loss in kinetic energy of the system in the process?

Five masses each of $2\, kg$ are placed on a horizontal circular disc, which can be rotated about a vertical axis passing through its centre and all the masses be equidistant from the axis and at a distance of $10\, cm$ from it. The moment of inertia of the whole system (in $gm-cm^2$) is (Assume disc is of negligible mass)

Two disc one of density $7.2\, g/cm^3$ and the other of density $8.9\, g/cm^3$ are of same mass and thickness. Their moments of inertia are in the ratio

$ ABC$  is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. $I_{AB}, I_{BC}, I_{CA}$  are the moment of inertia of the plate about $AB, BC$  and $CA$  respectively. Which one of the following relations is correct