RAJASTHAN ­ PET Rajasthan PET Solved Paper-2012

  • question_answer Two discs have same mass and thickness but are made, up of different materials having different densities. Which one of them will have larger moment of inertia?

    A)  Both disc have same moment of inertia

    B)  disc having less density have larger moment of inertia

    C)  disc having more density have larger moment of inertia

    D)  None of the above

    Correct Answer: B

    Solution :

     Since mass of both the disc is same \[\therefore \] \[\pi r_{1}^{2}t{{\rho }_{1}}=\pi r_{2}^{2}t{{\rho }_{2}}\] (\[\because \] Mass = volume\[\times \]density = area\[\times \]thickness\[\times \]density) \[\Rightarrow \] \[\frac{{{\rho }_{1}}}{{{\rho }_{2}}}=\frac{r_{2}^{2}}{r_{1}^{2}}\] \[\therefore \] \[\frac{{{I}_{1}}}{{{I}_{2}}}=\frac{\frac{1}{2}Mr_{1}^{2}}{\frac{1}{2}Mr_{2}^{2}}\] \[=\frac{r_{1}^{2}}{r_{2}^{2}}=\frac{{{\rho }_{2}}}{{{\rho }_{1}}}\] i.e., \[I\propto \frac{1}{\rho }\] So, the disc having less density have larger moment of inertia.

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