Question 364: Gravitation

Question

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

Accepted Answer

For the particle to escape from earth's gravitational field, it should be given kinetic energy equal to its binding energy.
$$\begin{aligned}
& 	herefore \quad \frac{1}{2} \mathrm{mv}^2=\frac{\mathrm{GMm}}{4 \mathrm{R}} \
& 	herefore \mathrm{V}=\left[\frac{\mathrm{GM}}{2 \mathrm{R}}ight]^{1 / 2}
\end{aligned}$$

Answer

$$\left[\frac{\mathrm{GM}}{2 \mathrm{R}}\right]^{1 / 2}$$

Answer

$$\left[\frac{\mathrm{gR}}{4}\right]^{1 / 2}$$

Answer

$$\left[\frac{2 \mathrm{~g}}{\mathrm{R}}\right]^{1 / 2}$$

Answer

$$\left[\frac{\mathrm{GM}}{\mathrm{R}}\right]^{1 / 2}$$

Gravitation

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

Choose the correct answer: