Three identical spherical shells, each of mass m and radius r are placed as shown in the figure. Consider an axis XX′ which is touching the two shells and passing through the diameter of the third shell. The moment of inertia of the system consisting of these three spherical shells about XX′ axis is:

Question

Three identical spherical shells, each of mass m and radius r are placed as shown in the figure. Consider an axis XX′ which is touching the two shells and passing through the diameter of the third shell. The moment of inertia of the system consisting of these three spherical shells about XX′ axis is: <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-sqyzpnj9ezeawqny.jpg" /> (A) (11/5)mr2 (B) 3mr2 (C) (16/5)mr2 (D) 4mr2

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-sqyzpnj9ezeasr7f.jpg" /> Total moment of inertia of the system, I=I1+I2+I3 I2=I3=(2/3)mr2+mr2=(5 m r2/3) I1=(2/3)mr2 ∴ I=2× 5(m r2/3)+(2/3)mr2 =(12 m r2/3)=4mr2

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

$3 m r^{2}$

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

$4 m r^{2}$

Total moment of inertia of the system,
$I = I_{1} + I_{2} + I_{3}$
$I_{2} = I_{3} = \frac{2}{3} m r^{2} + m r^{2} = \frac{5 m r ^{2}}{3}$
$I_{1} = \frac{2}{3} m r^{2}$
$∴ I = 2 \times 5 \frac{m r ^{2}}{3} + \frac{2}{3} m r^{2}$
$= \frac{12 m r ^{2}}{3} = 4 m r^{2}$

511​mr2

3mr2

516​mr2

4mr2

Total moment of inertia of the system, I=I1​+I2​+I3​ I2​=I3​=32​mr2+mr2=35mr2​ I1​=32​mr2 ∴I=2×53mr2​+32​mr2 =312mr2​=4mr2

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

$3 m r^{2}$

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

$4 m r^{2}$

Total moment of inertia of the system,
$I = I_{1} + I_{2} + I_{3}$
$I_{2} = I_{3} = \frac{2}{3} m r^{2} + m r^{2} = \frac{5 m r ^{2}}{3}$
$I_{1} = \frac{2}{3} m r^{2}$
$∴ I = 2 \times 5 \frac{m r ^{2}}{3} + \frac{2}{3} m r^{2}$
$= \frac{12 m r ^{2}}{3} = 4 m r^{2}$