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Two loops P and Q are made from a unifor...

Two loops P and Q are made from a uniform wire. The radii of P and Q are `R_(1) and R_(2)` respectively and their moments of inertia are `I_(P) and I_(Q)` respectively.
If `(I_(P))/(I_(Q))=8` then `(R_(1))/(R_(2))` is

A

5

B

4

C

3

D

2

Text Solution

Verified by Experts

The correct Answer is:
D
The length of the loop `P=2piR_(1)`
If x is the mass per unit length of the wire, then for P,
`M_(1)=2piR_(1)x`
Similarly for Q, `M_(2)=2piR_(2)x`
`(I_(P))/(I_(Q))=(M_(1)R_(1)^(2))/(M_(2)R_(2)^(2))=(2piR_(1)x.R_(1)^(2))/(2piR_(2)x.R_(2)^(2))=(R_(1)^(3))/(R_(2)^(3))`
`therefore" "8=((R_(1))/(R_(2)))^(3)" "(R_(1))/(R_(2))=2`
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