Question

Two rings have their moments of inertia in the ratio 2 : 1 and their diameters are in the ratio 2 : 1. The ratio of their masses will be:

• A. 2 : 1
• B. 1 : 2
• C. 1 : 4
• D. 1 : 1.

Answer 1

Answer: (B)

1 : 2

Answer 2

⇒ $I \propto m D ^ { 2 }$ Or $m \propto \frac { I } { D ^ { 2 } }$

$\frac { m _ { 1 } } { m _ { 2 } } = \frac { I _ { 1 } } { I _ { 2 } } \times \left( \frac { D _ { 2 } } { D _ { 1 } } \right) ^ { 2 } = \frac { 2 } { 1 } \left( \frac { 1 } { 2 } \right) ^ { 2 } = \frac { 2 } { 4 } = \frac { 1 } { 2 }$