Question

Two rings of radius R and nR made upof same material have the ratio of moment of inertia about an axis passing through centre is 1 : 8. The value of n is:

• A. 2
• B. $2 \sqrt { 2 }$
• C. 4
• D. ½

Answer 1

Answer: (A)

2

Answer 2

Ratio of moment of inertia of the rings

$\frac { I _ { 1 } } { I _ { 2 } } = \left( \frac { M _ { 1 } } { M _ { 2 } } \right) \left( \frac { R _ { 1 } } { R _ { 2 } } \right) ^ { 2 } = \left( \frac { \lambda l _ { 1 } } { \lambda l _ { 2 } } \right) \left( \frac { R _ { 1 } } { R _ { 2 } } \right) ^ { 2 }$ $= \left( \frac { 2 \pi R } { 2 \pi n R } \right) \left( \frac { R } { n R } \right) ^ { 2 }$

⇒$\frac { I _ { 1 } } { I _ { 2 } } = \frac { 1 } { n ^ { 3 } } = \frac { 1 } { 8 }$⇒ $n ^ { 3 } = 8$ ⇒ $n = 2$