Question

A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be:

• A. 800 km
• B. 1600 km
• C. 2133 km
• D. 4800 km

Answer 1

Answer: (A)

800 km

Answer 2

**As per the theory of conservation of energy **

$-\frac{ GM_em }{ R_e} + \frac{1}{2}m\bigg(\frac{1}{3}\sqrt{\frac{2Gm_e}{R_e)}}\bigg)^2 = - \frac{GM_em}{R_e+h}$

• $-\frac{GM_em}{R_e} + \frac{GM_em}{9R_e} = -\frac{GM_em}{R_e+h}$

$\frac{8}{9R_e} = \frac{1}{R_e+h}$

Therefore, the maximum height attained by the body will be:

$⇒ h = \frac{R_e}{8}$

= $\frac{6400}{8}$

= $800$ $km$