Masses and radii of earth and moon are M-1- M-2 and R-1- R-2 respectively- The distance between theircentre is -d- The minimum velocity given to mass -M- from the mid point of line joining their centre so that it will escape- -sqrt frac -4G-d- frac -M-1M-2-M-1-M-2- -sqrt frac -4G-M-1 - M-2-d- -sqrt frac -2G-d- left - frac -M-1-M-2-M-1M-2- right - sqrt-frac -2G-d-M-1-M-2-

Question

Toppr Admin · Accepted Answer

From conservation of energy- since the velocity will be 0 at infinity-12mv2-x2212-GmM1d-2-x2212-GmM2d-2-0v-2-x221A-G-M1-M2-dAnswer is option A-

Masses and radii of earth and moon are M1,M2 and R1,R2 respectively. The distance between theircentre is 'd'. The minimum velocity given to mass 'M' from the mid point of line joining their centre so that it will escape.√4GdM1M2(M1+M2)√4G(M1+M2)d√2Gd(M1+M2M1M2)√2Gd(M1+M2)

From conservation of energy, since the velocity will be 0 at infinity,12mv2−GmM1d/2−GmM2d/2=0v=2√G(M1+M2)dAnswer is option A.

From conservation of energy, since the velocity will be 0 at infinity,

$\frac{1}{2} m v^{2} - \frac{G m M_{1}}{d / 2} - \frac{G m M_{2}}{d / 2} = 0$

$v = 2 \sqrt{\frac{G (M_{1} + M_{2})}{d}}$

Answer is option A.