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The diameter of a disc is increased by 2...

The diameter of a disc is increased by `2%` without changing its mass. What is the percentage increase in its moment of inertia about its axis of symmetry?

A

`2%`

B

`4%`

C

`8%`

D

`1%`

Text Solution

Verified by Experts

The correct Answer is:
B
The M.I. of a disc about its axis of symmetry is
`I=(1)/(2)MR^(2)" "therefore" "logI=logM+2logR`
Differentiating, we get
`(dI)/(I)=0+2(dR)/(R)" "(because " M is constant")`
`therefore" Percentage change in M.I."`
`=(dI)/(I)xx100=2xx(dR)/(R)xx100`
`=2xx(2)/(100)xx100=4%`
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