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Rotational Motion question

2015 · Q134
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Rotational Motion question

2015 · Q134

NEETPhysicsRotational MotionMCQ+4 / −1
Three identical spherical shells, each of mass m and radius r are placed as shown in figure. 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

AIPMT 2015 Cancelled Paper Physics - Rotational Motion Question 73 English
  1. A
    165mr2{{16} \over 5}m{r^2}516​mr2
  2. B
    4mr2
  3. C
    115mr2{{11} \over 5}m{r^2}511​mr2
  4. D
    3mr2
View written solutionFree

Correct answer: B

Net moment of inertia of the system,

I = I1 + I2 + I3

The moment of inertia of a shell about its diameter,

I1 = 23{2 \over 3}32​mr2

The moment of inertia of a shell about its tangent is given by

I2=I3=I1+mr2=23mr2+mr2=53mr2{I_2} = {I_3} = {I_1} + m{r^2} = {2 \over 3}m{r^2} + m{r^2} = {5 \over 3}m{r^2}I2​=I3​=I1​+mr2=32​mr2+mr2=35​mr2

∴\therefore∴ I=2×53mr2+23mr2=12mr23=4mr2I = 2 \times {5 \over 3}m{r^2} + {2 \over 3}m{r^2} = {{12m{r^2}} \over 3} = 4m{r^2}I=2×35​mr2+32​mr2=312mr2​=4mr2

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