| Statement I \[{{I}_{S}}\] and \[{{I}_{H}}\] are the moments of inertia about the diameters of a solid and thin walled hollow sphere respectively. If the radii and the masses of the above spheres are equal, \[{{I}_{H}}>{{I}_{S}}\]. |
| Statement II In solid sphere, the mass is continuously and regularly distributed about the centre whereas the mass, to a large extent, is concentrated on the surface of hollow sphere. |
A) Both Statement I and Statement II are true and the Statement II is the correct explanation of the Statement I.
B) Both Statement I and Statement II are true but the Statement II is not the correct explanation of the Statement II.
C) Statement I is true but Statement II is false.
D) Both Statement I and Statement II are false.
Correct Answer: A
Solution :
The moment of inertia of solid sphere about its any diameter \[{{I}_{S}}=\frac{2}{5}\,M{{R}^{2}}\] The moment of inertia of a thin walled hollow sphere about its diameter is \[{{I}_{H}}=\frac{2}{5}M\,\frac{(R_{2}^{5}-R_{1}^{5})}{R_{2}^{3}-R_{1}^{3})},\] where \[{{R}_{1}}\], and \[{{R}_{2}}\] are its internal and external radii \[\therefore \] \[{{I}_{H}}>{{I}_{S}}\] The reason is that in solid sphere the whole mass is uniformly and continuously distributed about its centre in the entire volume while in hollow sphere the mass is distributed on the surface of sphere.
You need to login to perform this action.
You will be redirected in
3 sec
