A mass of 6 times 10^{24} ,kg is to be compre | vedclass

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Question

(D) The formula for escape velocity $v_e$ from the surface of a sphere of mass $M$ and radius $R$ is given by:
$v_e = \sqrt{\frac{2GM}{R}}$
Squaring

Vedclass · Accepted Answer

$888$

Vedclass · Answer

(D) The formula for escape velocity $v_e$ from the surface of a sphere of mass $M$ and radius $R$ is given by:
$v_e = \sqrt{\frac{2GM}{R}}$
Squaring both sides,we get:
$v_e^2 = \frac{2GM}{R}$
Rearranging to solve for $R$:
$R = \frac{2GM}{v_e^2}$
Given values:
$M = 6 	imes 10^{24} \,kg$
$v_e = 3 	imes 10^4 \,ms^{-1}$
$G = 6.66 	imes 10^{-11} \,N \,m^2 \,kg^{-2}$
Substituting the values:
$R = \frac{2 	imes 6.66 	imes 10^{-11} 	imes 6 	imes 10^{24}}{(3 	imes 10^4)^2}$
$R = \frac{79.92 	imes 10^{13}}{9 	imes 10^8}$
$R = 8.88 	imes 10^5 \,m$
Converting to kilometers:
$R = 888 \,km$
Thus,the correct option is $D$.

$A$ mass of $6 \times 10^{24} \,kg$ is to be compressed in the form of a solid sphere such that the escape velocity from its surface is $3 \times 10^4 \,ms^{-1}$. The radius of the sphere is (Universal gravitational constant $G = 6.66 \times 10^{-11} \,N \,m^2 \,kg^{-2}$) (in $\,km$)

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