JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Rotational Mechanics

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If a solid sphere of mass 5 kg and a disc of mass 4 kg have the same radius. Then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be

\frac{x}{7}

. The value of

x

is ____.

Answer: 5

Solution

For the sphere about a tangent, the parallel-axis theorem gives

I_{sph} = \frac{2}{5} m_{1} R^{2} + m_{1} R^{2} = \frac{7}{5} m_{1} R^{2} = \frac{7}{5} (5) R^{2} = 7 R^{2}

. For the disc about a tangent lying in its plane, the central-diameter value

\frac{1}{4} m_{2} R^{2}

shifts to

I_{disc} = \frac{1}{4} m_{2} R^{2} + m_{2} R^{2} = \frac{5}{4} m_{2} R^{2} = \frac{5}{4} (4) R^{2} = 5 R^{2}

. The ratio of the disc's moment to the sphere's is

\frac{5 R ^{2}}{7 R ^{2}} = \frac{5}{7}

, so

x = 5

JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Integer answer

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JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Rotational Mechanics

Solution

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