A) \[{{\rho }_{1}}:{{\rho }_{2}}\]
B) \[{{\rho }_{1}}:{{\rho }_{2}}:1\]
C) \[1:{{\rho }_{1}}\,\,{{\rho }_{2}}\]
D) \[{{\rho }_{2}}:{{\rho }_{1}}\]
Correct Answer: D
Solution :
Moment of inertia of disc \[I=\frac{1}{2}M{{R}^{2}}=\frac{1}{2}M\,\left( \frac{M}{\pi \rho t} \right)\] \[\therefore \] \[I=\frac{1}{2}\frac{{{M}^{2}}}{\pi \rho {{t}^{2}}}\] \[\left( As\,\,\rho =\frac{Mass}{Volume}=\frac{M}{\pi {{R}^{2}}t},\,\,therefore,\,{{R}^{2}}=\frac{M}{\pi \rho t} \right)\] \[\therefore \] \[I\propto \frac{1}{\rho }\] (If M and t are constants) \[\Rightarrow \] \[\frac{{{I}_{1}}}{{{I}_{2}}}=\frac{{{\rho }_{2}}}{{{\rho }_{1}}}\]
You need to login to perform this action.
You will be redirected in
3 sec
