PYQ Vault

Moment of inertia of a system of identical spheres about a given axis

This type of question, asked 7 times: 10 May 2024 S2, 13 May 2024 S2, 14 May 2024 S2, 20 Apr 2025 S1, 21 Apr 2025 S1, 17 Apr 2026 S1, 12 May 2026 S1. All 7 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    10 May 2024 S2

    29
    Two spheres each of mass 'MM' and radius R2\frac{R}{2} are connected at the ends of massless rod of length '2R2R'. What will be the moment of inertia of the system about an axis passing through centre of one of the spheres and perpendicular to the rod?

    Tap an option to check your answer.

  2. Question 2

    13 May 2024 S2

    32
    Four identical uniform solid spheres each of same mass 'M' and radius 'R' are placed touching each other as shown in figure with centres A, B, C, D. IA,IB,IC,IDI_A, I_B, I_C, I_D are the moment of inertia of these spheres respectively about an axis passing through centre and perpendicular to the plane, then

    Tap an option to check your answer.

  3. Question 3

    14 May 2024 S2

    5
    Four identical uniform solid spheres each of same mass MM and radius RR are placed touching each other with centres A, B, C, D. IAI_A and IBI_B are the moment of inertia of these spheres respectively about an axis passing through centre and perpendicular to the plane. The difference in IAI_A and IBI_B is

    Tap an option to check your answer.

  4. Question 4

    20 Apr 2025 S1

    40
    Two spheres each of mass MM and radius RR are connected with a massless rod of length 4 R . The moment of inertia of the system about an axis passing through the center of one of the spheres and perpendicular to the rod will be

    Tap an option to check your answer.

  5. Question 5

    21 Apr 2025 S1

    44
    Three spheres, each of mass ' mm ' and radius ' rr ' are placed as shown in figure. Consider an axis YY′YY^{'}, which is touching two spheres and passing through the diameter of third sphere. The moment of inertia of the system consisting of these three spheres about YY′YY^{'} axis is

    Tap an option to check your answer.

  6. Question 6

    17 Apr 2026 S1

    106
    A system of five solid spheres each of mass 'mm' and radius 'rr' are rotating about an axis AA' as shown in figure. Hence the moment of inertia of the system about the axis of rotation AA' is

    Tap an option to check your answer.

  7. Question 7

    12 May 2026 S1

    105
    Four solid spheres, each of diameter 5\sqrt{5} cm and mass 0.50.5 kg are placed with their centres at the corners of a square of side 44 cm. The M.I. of the system about the diagonal of the square is N×10−4N \times 10^{-4} kg-m2^2, then NN is

    Tap an option to check your answer.