The escape velocity of a body from the surfac | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The formula for escape velocity is given by $v_e = \sqrt{\frac{2GM}{R}}$.Since the mass $M$ of a planet can be expressed in terms of its density $

Vedclass · Accepted Answer

$22.4$

Vedclass · Answer

(C) The formula for escape velocity is given by $v_e = \sqrt{\frac{2GM}{R}}$.Since the mass $M$ of a planet can be expressed in terms of its density $ho$ and radius $R$ as $M = \frac{4}{3} \pi R^3 ho$,we substitute this into the formula:$v_e = \sqrt{\frac{2G(\frac{4}{3} \pi R^3 ho)}{R}} = \sqrt{\frac{8}{3} G \pi R^2 ho} = R \sqrt{\frac{8}{3} G \pi ho}$.From this expression,we see that $v_e \propto R$ when the density $ho$ is constant.Given that the planet has the same density as the earth but twice the radius $(R' = 2R_e)$,the new escape velocity $v_e'$ is:$v_e' = 2 	imes v_e = 2 	imes 11.2 \,km/s = 22.4 \,km/s$.

The escape velocity of a body from the surface of the earth is $11.2 \,km/s$. The escape velocity of a body from a planet having the same mean density as the earth but twice the radius of earth is: (in $\,km/s$)

Similar Questions

$A$ body is projected vertically upwards from the surface of a planet of radius $R$ with a velocity equal to half the escape velocity of that planet. Then,the maximum height attained by the body is

The radius and mean density of a planet are four times that of the Earth. The ratio of the escape velocity on the Earth to the escape velocity on the planet is:

$A$ rocket is launched with velocity $10 \ km/s$. If the radius of the Earth is $R$,then the maximum height attained by it will be: (in $R$)

If $M$ is the mass of a planet and $R$ is its radius,then in order to become a black hole (where $c$ is the speed of light),which condition must be satisfied?

$A$ certain object is projected vertically from the surface of the earth of radius $R$ with a velocity equal to half the escape velocity. The maximum height attained by the object will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module