Question

Q] In a certain unit, the radius of gyration of a uniform disc about its central and transverse axis is √2.5. Its radius of gyration about a tangent in its plane (in the same unit) must be

a)√5
b)2.5
c) 2√2.5
d)12.5​

Answer 1

${\large{\bold{\sf{\underline{GIVEN \; QUESTION:-}}}}}$

Q] In a certain unit, the radius of gyration of a uniform disc about its central and transverse axis is √2.5. Its radius of gyration about a tangent in its plane (in the same unit) must be

a)√5

b)2.5

c) 2√2.5

d)12.5

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${\large{\bold{\sf{\underline{LET'S \: UNDERSTAND \: THE \: QUESTIONS \: FIRST:-}}}}}$

Concept : Characteristics of Circular Motion

in the question it is given that In a certain unit,

• the radius of gyration of a uniform disc about its central

• transverse axis is √2.5

and we need to find Its radius of gyration about a tangent in its plane (in the same unit).

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

${\large{\bold{\sf{\underline{ANSWER:-}}}}}$

a)√5

b)2.5 ☑️

c) 2√2.5

d)12.5

In a certain unit, the radius of gyration of a uniform disc about its central and transverse axis is √2.5. Its radius of gyration about a tangent in its plane (in the same unit) must be 2.5

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

${\large{\bold{\sf{\underline{SOLUTION:-}}}}}$

CASE 1-

movement inertia of disc about an Axis through its centre is $\tt I = \dfrac{MR^{2} }{2}$

Now we know that ,

$\tt K = \dfrac{R}{ \sqrt{2} }$

and we know that the value of K is √2.5

$\tt K = \sqrt{ 2.5} \: (given)$

$\therefore \sf R = \sqrt{2K}$

$\longrightarrow \sf R = \sqrt{2} \times \sqrt{2.5}$

$\longrightarrow \sf R = \sqrt{5}$

CASE 2 -

now we know that the value of R is √5

so ,

$\tt K' = \dfrac{ \sqrt{5} R}{2}$

$\longrightarrow \tt K' = \dfrac{ \sqrt{5} \times \sqrt{5} }{2}$

$\longrightarrow \tt 2.5$

Therefore , radius of gyration about a tangent in its plane (in the same unit) must be 2.5

B option is correct

Answer 2

Q] In a certain unit, the radius of gyration of a uniform disc about its central and transverse axis is √2.5. Its radius of gyration about a tangent in its plane (in the same unit) must be

a)√5

b)2.5 (answer)

c) 2√2.5

d)12.5

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