Three-point masses 'm' each, are placed at the vertices of an equilateral triangle of side a. Moment of inertia of the system about axis COD is-

1. $2m{a}^2$

2. $\frac{2}{3}m{a}^2$

3. $\frac{5}{4}m{a}^2$

4. $\frac{7}{4}m{a}^2$

One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively I_A and I_B such that

1. ${\mathrm{I}}_{\mathrm{A}}={\mathrm{I}}_{\mathrm{B}}$

2. ${\mathrm{I}}_{\mathrm{A}}>{\mathrm{I}}_{\mathrm{B}}$

3. ${\mathrm{I}}_{\mathrm{A}}<{\mathrm{I}}_{\mathrm{B}}$

4. $\frac{{\mathrm{I}}_{\mathrm{A}}}{{\mathrm{I}}_{\mathrm{B}}}=\frac{d_A}{d_B}$

A particle of mass 1 kg is kept at (1m, 1m, 1m). The moment of inertia of this particle about z-axis would be

1.  $1 \mathrm{kg}-{\mathrm{m}}^2$

2.  $2 \mathrm{kg}-{\mathrm{m}}^2$

3.  $3 \mathrm{kg}-{\mathrm{m}}^2$

4.  None of these

One-quarter sector is cut from a uniform circular disc of radius R.  This sector has mass M.  It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc.  Its moment of inertia about the axis of rotation is:

1. $\frac{1}{2}M{R}^2$

2. $\frac{1}{4}M{R}^2$

3. $\frac{1}{8}M{R}^2$

4. $\sqrt{2}M{R}^2$

The radius of gyration of a uniform rod of length L about an axis passing through its centre of mass is

1. $\frac{L}{2\sqrt{3}}$

2. $\frac{L^2}{12}$

3. $\frac{L}{\sqrt{3}}$

4. $\frac{L}{\sqrt{2}}$