Question

If the radius of the earth reduces by 4%, density remaining the same, then the escape velocity will:

• A. increases by $4$ %
• B. increases by $2$%
• C. decreases by $4$ %
• D. decreases by $2$ %

Answer 1

Answer: (C)

decreases by $4$ %

expression for escape velocity from sun is given by $\sqrt{\frac{2GM}{R}}$

can be rewritten in the form of density ($\sigma$) and radius of earth.

$V_e=\sqrt{2G\sigma .R^2}$

so escape velocty depends on $\sqrt{density}$ and $radius$

so if radius is reduced then escape velocity will be decreased in the same ratio.

so best possibkle option is option C.