Question

If the radius of earth contracts $\frac { 1 } { n }$ of its present value, the length of the day will be approximately

• A. $\frac { 24 } { n } h$
• B. $\frac { 24 } { n ^ { 2 } } h$
• C. $24 n h$
• D. $24 n ^ { 2 } h$

Answer 1

Answer: (B)

$\frac { 24 } { n ^ { 2 } } h$

Answer 2

Conservation of angular momentum $L = I \omega =$

$= \frac { 2 } { 5 } M R ^ { 2 } \times \frac { 2 \pi } { T } =$ constant ∴ $T \propto R ^ { 2 }$

[If M remains same]

⇒ $\frac { T _ { 2 } } { T _ { 1 } } = \left( \frac { R _ { 2 } } { R _ { 1 } } \right) ^ { 2 }$ $= \left( \frac { R / n } { R } \right) ^ { 2 }$ $= \frac { 1 } { n ^ { 2 } }$ ⇒ $T _ { 2 } = \frac { 24 } { n ^ { 2 } } h r$

[As].