System Of Particles And Rotational Motion Ques 57
57. 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
(a) $3 $ $mr^{2}$
(b) $\frac{16}{5} $ $mr^{2}$
(c) $4 $ $mr^{2}$
(d) $\frac{11}{5} $ $mr^{2}$
[2015]
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Answer:
Correct Answer: 57.(c)
Solution:
- (c) Moment of inertia of shell $1$ along diameter
$I _{\text{diameter }}=\frac{2}{3} Mr^{2}$
Moment of inertia of shell $2=$ M.I of shell $3$
$=I _{\text{tangential }}=\frac{2}{3} Mr^{2}+Mr^{2}=\frac{5}{3} $ $Mr^{2}$
So, I of the system along $XX^{\prime}$
$=I _{\text{diameter }}+(I _{\text{tangential }}) \times 2$
or, $I _{\text{total }}=\frac{2}{3} Mr^{2}+(\frac{5}{3} Mr^{2}) \times 2$
$=\frac{12}{3} Mr^{2}=4 $ $Mr^{2}$
BETA
