Question 162: Gravitation

Question

The masses and radii of the earth and moon are (M1, R1) and (M2, R2) respectively. Their centres are at a distance 'r' apart. Find the minimum escape velocity for a particle of mass 'm' to be projected from the middle of these two masses :

Accepted Answer

$${1 \over 2}m{V^2} - {{G{M_1}m} \over {r/2}} - {{G{M_2}m} \over {r/2}} = 0$$
$${1 \over 2}m{V^2} = {{2Gm} \over r}({M_1} + {M_2})$$
$$V = \sqrt {{{4G({M_1} + {M_2})} \over r}} $$
Option (b)

Answer

$$V = {1 \over 2}\sqrt {{{4G({M_1} + {M_2})} \over r}} $$

Answer

$$V = \sqrt {{{4G({M_1} + {M_2})} \over r}} $$

Answer

$$V = {1 \over 2}\sqrt {{{2G({M_1} + {M_2})} \over r}} $$

Answer

$$V = {{\sqrt {2G} ({M_1} + {M_2})} \over r}$$

Gravitation

The masses and radii of the earth and moon are (M1, R1) and (M2, R2) respectively. Their centres are at a distance 'r' apart. Find the minimum escape velocity for a particle of mass 'm' to be projected from the middle of these two masses :

Choose the correct answer: