SATHEE: Gravitation Question 350

Gravitation Question 350

Question: The radius of the earth is reduced by 4%. The mass of the earth remains unchanged. What will be the change in escape velocity?

Options:

A) Increased by 2%

B) Decreased by 4%

C) Increased by 6%

D) Decreased by 8%

Show Answer

Answer:

Correct Answer: A

Solution:

Escape velocity $[= v = \sqrt{\frac{2 G M}{R}}]$

$[\Rightarrow v^{2} = \frac{2 G M}{R}]$ ….(i)

$[v^{2} = (2 G M) R^{- 1}]$

Differentiating both sides, we get,

$[2 v \frac{d v}{d R} = - \frac{2 G M}{R^{2}} \Rightarrow v \frac{d v}{d R} = \frac{G M}{R^{2}}]$ ….(ii) Dividing (ii) by (i),

$[\frac{1}{v} \frac{d v}{d R} = - \frac{1}{2 R}]$

$[\Rightarrow | \frac{d v}{v} | \times 100 = \frac{1}{2} \times 4 = 2]$ %

$[∴]$ If the radius decreases by 4%, escape velocity will increase by 2%.

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Gravitation Question 350

Question: The radius of the earth is reduced by 4%. The mass of the earth remains unchanged. What will be the change in escape velocity?

Options:

Answer:

Solution:

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