The escape velocity for the earth is 11.2 km | vedclass

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(D) The formula for escape velocity is $v = \sqrt{\frac{2GM}{R}}$.Given that the escape velocity of the earth is $v_e = 11.2 \ km/s$.For another plane

Vedclass · Accepted Answer

$56.0$

Vedclass · Answer

(D) The formula for escape velocity is $v = \sqrt{\frac{2GM}{R}}$.Given that the escape velocity of the earth is $v_e = 11.2 \ km/s$.For another planet,the mass $M_p = 100 M_e$ and the radius $R_p = 4 R_e$.The ratio of escape velocities is $\frac{v_p}{v_e} = \sqrt{\frac{M_p}{M_e} 	imes \frac{R_e}{R_p}}$.Substituting the given values: $\frac{v_p}{v_e} = \sqrt{\frac{100 M_e}{M_e} 	imes \frac{R_e}{4 R_e}} = \sqrt{100 	imes \frac{1}{4}} = \sqrt{25} = 5$.Therefore,$v_p = 5 	imes v_e = 5 	imes 11.2 \ km/s = 56.0 \ km/s$.

The escape velocity for the earth is $11.2 \ km/s$. The mass of another planet is $100$ times that of the earth and its radius is $4$ times that of the earth. The escape velocity for this planet will be ......... $km/s$.

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