$A$ particle of mass $m$ is kept at rest at a height $3R$ from the surface of the Earth,where $R$ is the radius of the Earth and $M$ is the mass of the Earth. The minimum speed with which it should be projected upward so that it does not return back is ($g$ = acceleration due to gravity on the Earth's surface).

  • A
    $[\frac{GM}{2R}]^{1/2}$
  • B
    $[\frac{gR}{4}]^{1/2}$
  • C
    $[\frac{2g}{R}]^{1/2}$
  • D
    $[\frac{GM}{R}]^{1/2}$

Explore More

Similar Questions

Let the escape velocity of a body kept at the surface of a planet be $u$. If it is projected at a speed of $200 \%$ more than the escape speed,then its speed in interstellar space will be ...........

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: Earth has an atmosphere,whereas the Moon does not have any atmosphere.
Reason $R$: The escape velocity on the Moon is very small compared to that on the Earth.
In the light of the above statements,choose the correct answer from the options given below:

Maximum height reached by a rocket fired with a speed equal to $50 \%$ of the escape speed from the surface of the earth is ($R$ - Radius of the earth).

The escape velocity of an object from a planet is $16 \ km/s$. If the escape velocity of the object from another planet having twice the density and three times the radius of the planet is $v \sqrt{2} \ km/s$,then the value of $v$ is

If the radius of a planet is $R$ and its density is $\rho$,the escape velocity from its surface will be

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo