Moment of Inertia

The moment of inertia of a thin uniform rod about an
axis passing through its centre and perpendicular to
its length is  $I_0$   . What is the M.I. about an axis through
one end and ⊥ the rod ?

•  $0.5I_0$  

•  $3I_0$  

•  $5I_0$  

•  $4I_0$  

Two rings of the same mass and radius 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

(Take M = mass of each ring and R = radius of each

ring)

• $MR^2$

• $\frac{3}{2}MR^2$

• $2MR^2$

• $\frac{5}{2}MR^2$

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

• $2ma^2$

• $\frac{2}{3}ma^2$

• $\frac{5}{4}ma^2$

• $\frac{7}{4}ma^2$

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 kg.m2

• 2 kg.m2

• 3 kg.m2

• 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 as shown is

• $\frac{1}{2}MR^2$

• $\frac{1}{4}MR^2$

• $\frac{1}{8}MR^2$

• $\frac{1}{16}MR^2$

Two uniform, thin identical rods each of mass M and length I are joined together to form a cross. What will be the moment of inertia of the cross about an axis passing through the point at which the two rods are joined and perpendicular to the plane of the cross?

• $\frac{Ml^2}{12}$

• $\frac{Ml^2}{6}$

• $\frac{Ml^2}{4}$

• $\frac{Ml^2}{3}$

The figure shows a uniform solid block of mass M and edge lengths a, b and c. Its M.O.I. about an axis through one edge and perpendicular (as shown) to the large face of the block is

• $\frac{M}{3}\left(a^2+b^2\right)$

• $\frac{M}{4}\left(a^2+b^2\right)$

• $\frac{M}{9}\left(a^2+b^2\right)$

• $\frac{M}{12}\left(a^2+b^2\right)$

The moment of inertia of a cube of mass m and side a about one of its edges is equal to

• $\frac{2}{3}ma^2$

• $\frac{4}{3}ma^2$

• $\frac{6}{3}ma^2$

• $\frac{8}{3}ma^2$