Parallel and perpendicular axes theorems — NEET & JEE Questions

Question 1 · difficulty L1 · recall

The parallel-axis theorem for moment of inertia is

• A. $I=I_{CM}+Md^2$
• B. $I=I_{CM}-Md^2$
• C. $I=Md$
• D. $I=I_{CM}+Md$

Question 2 · difficulty L2 · understanding

The perpendicular-axis theorem is applicable to

• A. a plane lamina
• B. any arbitrary three-dimensional body
• C. only a point mass
• D. only a sphere

Question 3 · difficulty L2 · understanding

For a plane lamina in the xy-plane, the perpendicular-axis theorem gives

• A. $I_z=I_x+I_y$
• B. $I_x=I_y+I_z$
• C. $I_z=I_x-I_y$
• D. $I_xI_y=I_z$

Question 4 · difficulty L2 · understanding

In the parallel-axis theorem, $d$ represents

• A. the perpendicular distance between the two parallel axes
• B. the radius of the body
• C. the distance from every particle to the axis
• D. the diameter of gyration

Question 5 · difficulty L3 · application

A body of mass 2 kg has moment of inertia $0.50\,\text{kg m}^2$ about a centre-of-mass axis. What is its moment of inertia about a parallel axis 0.30 m away?

• A. 0.18 kg m²
• B. 0.50 kg m²
• C. 0.68 kg m²
• D. 0.80 kg m²

Question 6 · difficulty L3 · application

A thin circular disc has moment of inertia $I_z=\frac12MR^2$ about its central axis perpendicular to the plane. By symmetry $I_x=I_y$. What is $I_x$ about a diameter?

• A. $\frac14MR^2$
• B. $\frac12MR^2$
• C. $MR^2$
• D. $\frac18MR^2$

Question 7 · difficulty L3 · application

A thin ring has moment of inertia $MR^2$ about its central axis perpendicular to its plane. What is its moment of inertia about any diameter?

• A. $\frac12MR^2$
• B. $MR^2$
• C. $2MR^2$
• D. $\frac14MR^2$

Question 8 · difficulty L3 · application

A rod has centre-of-mass moment of inertia $ML^2/12$ about an axis perpendicular to its length. What is the moment of inertia about a parallel axis through one end?

• A. $ML^2/3$
• B. $ML^2/12$
• C. $ML^2/4$
• D. $7ML^2/12$

Question 9 · difficulty L4 · application

A uniform disc of mass M and radius R has moment of inertia $MR^2/4$ about a diameter. What is its moment of inertia about an axis parallel to this diameter and tangent to the disc?

• A. $\frac54MR^2$
• B. $\frac12MR^2$
• C. $\frac34MR^2$
• D. $\frac32MR^2$

Question 10 · difficulty L4 · application

For a thin rectangular lamina, moments about two perpendicular in-plane axes through the centre are $I_x=2$ and $I_y=3$ kg m². What is the moment about the perpendicular central axis?

• A. 1 kg m²
• B. 5 kg m²
• C. 6 kg m²
• D. 9 kg m²