A) 5 : 7
B) 3 : 5
C) \[\sqrt{3}\,:\,\sqrt{5}\]
D) \[\sqrt{3}\,:\,\sqrt{7}\]
Correct Answer: C
Solution :
Let the radii of the thin spherical shell and the solid sphere are \[{{R}_{1}}\] and \[{{R}_{2}}\] respectively. Then, the moment of inertia of the spherical shell about one of their diameters \[I=\frac{2}{3}\,MR_{1}^{2}\] ...(i) and the moment of inertia of the solid sphere about one of their diameters (respective to first one) is given by \[I=\frac{2}{5}MR_{2}^{2}\] ...(ii) It is given that the masses and moment of inertia for both the bodies are equal, then from Eqs. (i) and (ii) \[\frac{2}{3}\,MR_{1}^{2}=\frac{2}{5}MR_{2}^{2}\] \[\Rightarrow \] \[\frac{R_{1}^{2}}{R_{2}^{2}}=\frac{3}{5}\] \[\Rightarrow \] \[\frac{{{R}_{1}}}{{{R}_{2}}}=\sqrt{\frac{3}{5}}\] \[\Rightarrow \] \[{{R}_{1}}\,:\,\,{{R}_{2}}=\,\sqrt{3}\,:\,\sqrt{5}\]
You need to login to perform this action.
You will be redirected in
3 sec
