A rocket is launched straight up from the sur | vedclass

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

Question

(C) Let $R$ be the radius of the earth and $M$ be its mass. The escape velocity at the surface is $v_e = \sqrt{\frac{2GM}{R}} = 11.2 \ km/s$.When the

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(C) Let $R$ be the radius of the earth and $M$ be its mass. The escape velocity at the surface is $v_e = \sqrt{\frac{2GM}{R}} = 11.2 \ km/s$.When the rocket is at an altitude $h = \frac{R}{4}$,its distance from the center of the earth is $r = R + h = R + \frac{R}{4} = \frac{5R}{4}$.To escape the earth's gravitational pull from this point,the rocket must have a velocity $v'$ such that its total energy is at least zero.Using the conservation of energy: $\frac{1}{2}mv'^2 - \frac{GMm}{r} = 0$.$v' = \sqrt{\frac{2GM}{r}} = \sqrt{\frac{2GM}{5R/4}} = \sqrt{\frac{8GM}{5R}} = \sqrt{\frac{4}{5}} 	imes \sqrt{\frac{2GM}{R}}$.Substituting $v_e = 11.2 \ km/s$:$v' = \sqrt{0.8} 	imes 11.2 \approx 0.8944 	imes 11.2 \approx 10.02 \ km/s$.Thus,the minimum velocity is approximately $10 \ km/s$.

Similar Questions

If the acceleration due to gravity $g$ doubles and the radius of earth becomes half that of the present value,then the value of escape velocity is (Assume,$g=10 \ m/s^2$ and radius of earth,$R=6400 \ km$)

Why does a rocket not have escape energy?

The mass and radius of the earth and moon are $M, R$ and $m, r$ respectively. The distance between their centers is $d$. The minimum velocity with which a particle of mass $m_0$ should be projected from the midpoint between them so that it could reach infinity is

An object is kept at rest at a distance of $3R$ above the earth's surface,where $R$ is the earth's radius. The minimum speed with which it must be projected so that it does not return to earth is (Assume $M =$ mass of earth,$G =$ Universal gravitational constant).

The masses and radii of the Earth and Moon are $M_1, R_1$ and $M_2, R_2$ respectively. Their centres are at a distance $d$ apart. The minimum speed with which a body of mass $m$ should be projected from a distance $2d/3$ from the centre of $M_1$ so as to escape to infinity is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module