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JEE Main 202324 JanuaryMorning Shift
Exam
JEE Main
Year
2023
Date
24 January
Shift
Morning Shift
Subject
Physics
Chapter
Rotational Motion

JEE Main 2023 · 24 January · Morning Shift · Physics · Rotational Motion

Solid sphere A is rotating about an axis PQ . If the radius of the...

Solid sphere AA is rotating about an axis PQPQ. If the radius of the sphere is 5cm5cm, then its radius of gyration about PQPQ will be xcm\sqrt{x}cm. The value of xx is _____.

Solid sphere A is rotating about an axis PQ . If the radius of the sphere is 5cm , then its radius of gyration about PQ

Correct answer

0

Step-by-step solution

Solid sphere A is rotating about an axis PQ . If the radius of the sphere is 5cm , then its radius of gyration about PQ

Using parallel axis theorem,

IPQ=ICOM+Md2{I}_{PQ} = {I}_{\text{COM}} + M{d}^{2}

=25MR2+Md2= \dfrac{2}{5}M{R}^{2} + M{d}^{2}

=M[25×52+102]= M\left[\dfrac{2}{5} \times {5}^{2} + {10}^{2}\right]

=M[110]=Mk2= M [ 110 ] = M{k}^{2}

⇒k=110cm⇒ k = \sqrt{110}cm

Therefore, x=110x = 110.

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