Physics | JEE Main previous year questions with Solutions

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Q 21 :

The moment of inertia of a semicircular ring about an axis passing through the center and perpendicular to the plane of the ring is $\frac{1}{x} M R^{2},$ where R is the radius and M is the mass of the semicircular ring. The value of $x$ will be _______ . [2023]

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(1)

The moment of inertia of a semicircular ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is $= M R^{2}$

$So x = 1$

Q 22 :

A solid sphere and a solid cylinder of the same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyration respectively $(k_{sph} : k_{cyl})$ is $2 : \sqrt{x},$ then the value of $x$ is _________ . [2023]

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(5)

$For solid sphere, \frac{2}{5} m R^{2} = m k_{sph}^{2}$

$k_{sph} = \sqrt{\frac{2}{5}} R$

$For solid cylinder, \frac{m R^{2}}{2} = m k_{cyl}^{2}$

$\Rightarrow k_{cyl} = \frac{R}{\sqrt{2}}$

$\frac{k_{sph}}{k_{cyl}} = \frac{\sqrt{\frac{2}{5}}}{\frac{1}{\sqrt{2}}} = \frac{2}{\sqrt{5}} = \frac{2}{\sqrt{x}}$

$∴$ $x = 5$

Topic Question Set

Q 21 :

The moment of inertia of a semicircular ring about an axis passing through the center and perpendicular to the plane of the ring is $\frac{1}{x} M R^{2},$ where R is the radius and M is the mass of the semicircular ring. The value of $x$ will be _______ . [2023]

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Q 22 :

A solid sphere and a solid cylinder of the same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyration respectively $(k_{sph} : k_{cyl})$ is $2 : \sqrt{x},$ then the value of $x$ is _________ . [2023]

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