Question

An object is kept at rest at a distance of 3R above the earth’s surface where R is earth’s radius. The minimum speed with which it must be projected so that it does not return to earth is :

(Assume M = mass of earth, G = Universal gravitational constant)

(1) \(\sqrt{\frac{GM}{2R}}\)

(2) \(\sqrt{\frac{GM}{R}}\)

(3) \(\sqrt{\frac{3GM}{R}}\)

(4) \(\sqrt{\frac{2GM}{R}}\)

Answer 1

Correct option is : (1) \(\sqrt{\frac{GM}{2R}}\)
 

\(P_P +k_P = P_0 +k_0\)

\(-\frac{GMm}{4R} + \frac {1}{2} mV_P ^2 = 0\)

\(V_P = \sqrt{\frac{GM}{2R}}\)