A body is projected vertically from the surfa | vedclass

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

Question

(B) Let the mass of the body be $m$ and the mass of the earth be $M$. The escape velocity is $v_e = \sqrt{\frac{2GM}{R}}$.The initial velocity of the

Vedclass · Accepted Answer

$R/3$

Vedclass · Answer

(B) Let the mass of the body be $m$ and the mass of the earth be $M$. The escape velocity is $v_e = \sqrt{\frac{2GM}{R}}$.The initial velocity of the body is $v = \frac{v_e}{2} = \frac{1}{2} \sqrt{\frac{2GM}{R}}$.Using the law of conservation of mechanical energy between the surface of the earth and the maximum height $h$ (where final velocity is $0$):$K_i + U_i = K_f + U_f$$\frac{1}{2}mv^2 - \frac{GMm}{R} = 0 - \frac{GMm}{R+h}$Substituting $v^2 = \frac{1}{4} \cdot \frac{2GM}{R} = \frac{GM}{2R}$:$\frac{1}{2}m \left( \frac{GM}{2R} \right) - \frac{GMm}{R} = - \frac{GMm}{R+h}$$\frac{GMm}{4R} - \frac{GMm}{R} = - \frac{GMm}{R+h}$$-\frac{3GMm}{4R} = - \frac{GMm}{R+h}$$\frac{3}{4R} = \frac{1}{R+h}$$3(R+h) = 4R$$3R + 3h = 4R$$3h = R$$h = R/3$

$A$ body is projected vertically from the surface of the earth of radius $R$ with a velocity equal to half of the escape velocity. The maximum height reached by the body is

Similar Questions

The escape velocity for a planet whose mass is six times the mass of Earth and whose radius is twice the radius of Earth will be (where $V_{e}$ is the escape velocity from the Earth).

When the speed of a satellite is increased by $x$ percentage,it will escape from its orbit,where the value of $x$ is ....... $\%$

If the Earth has a mass nine times and a radius twice that of a planet $P$. Then $\frac{v_e}{3} \sqrt{x} \; ms^{-1}$ will be the minimum velocity required by a rocket to escape the gravitational force of $P$,where $v_e$ is the escape velocity on Earth. The value of $x$ is

$A$ planet in a distant solar system is $10$ times more massive than the earth and its radius is $10$ times smaller. Given that the escape velocity from the earth is $11 \ km/s$,the escape velocity from the surface of the planet would be ........ $km/s$.

If the acceleration due to gravity on the surface of a planet is two times that on the surface of the Earth and its radius is double that of the Earth,then the escape velocity from the surface of that planet in comparison to the Earth will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module