A solid sphere of mass 500 g and radius 5 cm is rotated about one of its diameter with angular speed of 10 rad . If the moment of inertia of the sphere about its tangent is times its angular momentum about the diameter, then the value of will be _______

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Solution

Q.
A solid sphere of mass 500 g and radius 5 cm is rotated about one of its diameter with angular speed of 10 rad $s^{- 1}$ . If the moment of inertia of the sphere about its tangent is $x \times 10^{- 2}$ times its angular momentum about the diameter, then the value of $x$ will be ________. [2023]

Ans.
(35)

$m = 500 g = 0.5 kg$

$R = 5 cm$

$ω = 10 rad/s$

$Moment of inertia about tangent = I_{T}$

$I_{T} = x \times 10^{- 2} L$

$\frac{7}{5} m R^{2} = x \times 10^{- 2} \frac{2}{5} m R^{2} ω$

$\frac{7}{2 ω} = x \times 10^{- 2} = \frac{7}{2 \times 10}$

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