Physics | JEE Main previous year questions with Solutions

(199)

All bodies have same mass and same radius.

Disk, $I_{A} = \frac{m R^{2}}{4} = I$

Solid sphere, $I_{B} = \frac{7}{5} m R^{2}$

Spherical shell, $I_{C} = \frac{5}{3} m R^{2}$

$I_{P Q} = \frac{m R^{2}}{4} + (\frac{2}{5} m R^{2} + m R^{2}) + (\frac{2}{3} m R^{2} + m R^{2})$

$I_{P Q} = \frac{15 m R^{2} + 24 m R^{2} + 60 m R^{2} + 40 m R^{2} + 60 m R^{2}}{60}$

$I_{P Q} = \frac{199}{60} m R^{2} = \frac{199}{15} (\frac{m R^{2}}{4}) = \frac{199}{15} I$

(9)

Without cavity $I_{1} = \frac{M R^{2}}{2}$

Mass of removed disc = $\frac{M}{π R^{2}} \times {(\frac{R}{3})}^{2} π = (\frac{M}{9})$

M.I. of removed disc $I_{2} = \frac{\frac{M}{9} {(\frac{R}{3})}^{2}}{2} + \frac{M}{9} \times {(\frac{2 R}{3})}^{2} = \frac{M R^{2}}{18}$

$I_{(remaining part)} = I_{1} - I_{2} = \frac{M R^{2}}{2} - \frac{M R^{2}}{18} = \frac{4 M R^{2}}{9} \Rightarrow x = 9$

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