Questions

Three identical spherical shells, each of mass *m* and radius *r* are placed as shown in figure. Consider an axis *XX'*, which is touching the 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 [CBSE AIPMT 2015]

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a

115mr2

b

3 mr2

c

165mr2

d

4 mr2

detailed solution

Correct option is D

The total moment of inertia of the system,I=I1+I2+I3 …(i)Here, I1=23mr2I2=I3=23mr2+mr2 (From parallel axes theorem)=53mr2From Eq. (i), we getI=23mr2+2×53mr2=mr223+103⇒I=4mr2

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A rectangular loop has mass M and sides a and b. An axis ${\mathrm{OO}}^{\text{'}}$ passes tlrrough the centre C of the loop and is parallel to side a (lie in the plane of the loop). Then the radius of gyration of the loop, for the axis ${\mathrm{OO}}^{\text{'}}$ is

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