A sphere of mass 10 ~kg and radius 0.5 ~m rotates about a tangent. The moment of inertia of the sphere is

Correct answer: C. 3.5 ~kg ~m^2 M.I. about tangent =I+M R^2 aligned & =(2)/(5) M R^2+M R^2=(7)/(5) M R^2 & =(7)/(5) ×(10) ×(0.5)^2=3.5 ~kg ~m^2 aligned

AIIMS 2016

Exam: AIIMS
Year: 2016
Subject: Physics
Chapter: Rotational Motion

AIIMS 2016 · Physics · Rotational Motion

A sphere of mass 10 ~kg and radius 0.5 ~m rotates about a tangent....

A sphere of mass

10 \mathrm{~kg}

and radius

0.5 \mathrm{~m}

rotates about a tangent. The moment of inertia of the sphere is

Options

A $5 \mathrm{~kg} \mathrm{~m}^2$
B $2.7 \mathrm{~kg} \mathrm{~m}^2$
C $3.5 \mathrm{~kg} \mathrm{~m}^2$
D $4.5 \mathrm{~kg} \mathrm{~m}^2$

Correct answer

C. $3.5 \mathrm{~kg} \mathrm{~m}^2$

Step-by-step solution

M.I. about tangent

=I+M R^2

\begin{aligned} & =\frac{2}{5} M R^2+M R^2=\frac{7}{5} M R^2 \\ & =\frac{7}{5} \times(10) \times(0.5)^2=3.5 \mathrm{~kg} \mathrm{~m}^2\end{aligned}

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