Question

A body of mass m is projected with velocity λv_e in vertically upward direction from the surface of the earth into space. It is given that v_e is escape velocity and λ< 1. If air resistance is considered to be negligible, then the maximum height from the centre of earth, to which the body can go, will be:
(R : radius of earth)

• A. \(\frac{R}{1+λ^2}\)
• B. \(\frac{R}{1-λ^2}\)
• C. \(\frac{R}{1-λ}\)
• D. \(\frac{λ^2R}{1-λ^2}\)

Answer 1

The Correct Option is B

The correct answer is (B): \(\frac{R}{1-λ^2}\)
Using energy conservation
\(-\frac{GM_em}{R_e} + \frac{1}{2}m \left(λ\sqrt{\frac{2GM_e}{R_e}} \right)^2 = -\frac{GM_em}{r}\)
\(\frac{GM_em}{r} = \frac{GM_em}{R_e} - \frac{GM_em}{R_e} λ^2\)
\(r = \frac{R_e}{1-λ^2}\)