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NEET 2024

Exam: NEET
Year: 2024
Subject: Physics
Chapter: Rotational Motion

NEET 2024 · Physics · Rotational Motion

The radius of gyration of a solid sphere of mass 5 kg about X Y is...

The radius of gyration of a solid sphere of mass 5 kg about

X Y

is 5 m as shown in figure. The radius of the sphere is

\frac{5 x}{\sqrt{7}} \mathrm{~m}

, then the value of

x

is:

The radius of gyration of a solid sphere of mass 5 kg about X Y is 5 m as shown in figure. The radius of the sphere is

Options

A5
B $\sqrt{2}$
C $\sqrt{2}$
D $\sqrt{5}$

Correct answer

D. $\sqrt{5}$

Step-by-step solution

I_{X Y}=I_{C M}+M R^2=\frac{2}{5} M R^2+M R^2=\frac{7}{5} M R^2=\frac{7}{5} \times 5 R^2=7 R^2

...(1)

I_{X Y}=M K^2=5 \times 5^2

...(ii)

\therefore 5 \times 5^2=7 \times R^2 \quad[

From (1) and (2)]

\Rightarrow R=\sqrt{\frac{5}{7}} \times 5=\frac{5 x}{\sqrt{7}} \quad

(Given)

\therefore x=\sqrt{5}

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