SATHEE: Rotational Motion Question 84

Rotational Motion Question 84

Question: Three identical spherical shells, each of mass m and radius r.Consider an axis XX, which is touching to two shells and passing through diameter of third shell.Moment of inertia of the system consisting of these three spherical shells about XX axis is

Options:

A) $\frac{11}{5} m r^{2}$

B) $3 m r^{2}$

C) $\frac{16}{5} m r^{2}$

D) $4 m r^{2}$

Show Answer

Answer:

Correct Answer: D

Solution:

The total moment of inertia of the system is

$I = I_{1} + I_{2} + I_{3}$ ..(i)

Hero $I_{1} = \frac{2}{3} m r^{2}$

$I_{2} = I_{3} = \frac{2}{3} m r^{2} + m r^{2}$

(From parallel axis theorem]

$= \frac{5}{3} m r^{2}$

From Eq.(i),

$I = \frac{2}{3} m r^{2} + 2 \times \frac{5}{3} m r^{2} = m r^{2} (\frac{2}{3} + \frac{10}{3})$

$I = 4 m r^{2}$

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Rotational Motion Question 84

Question: Three identical spherical shells, each of mass m and radius r.Consider an axis XX, which is touching to two shells and passing through diameter of third shell.Moment of inertia of the system consisting of these three spherical shells about XX axis is

Options:

Answer:

Solution:

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Question: Three identical spherical shells, each of mass m and radius r.Consider an axis XX, which is touching to two shells and passing through diameter of third shell.Moment of inertia of the system consisting of these three spherical shells about XX axis is