A satellite revolving around earth in a circular orbit of radius 4R. Due to ejection of a rocket the speed of satellite is reduced to half as a result of which satellite starts falling toward earth. Find the angle at which it will hit the earth surface.

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

$θ = 37^{o}$

$θ = 33^{o}$

$θ = 40^{o}$

$θ = 32^{o}$

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

with respect to earth, we conserve energy and angular momentum

$m (\frac{v}{2}) 4 R = m (v_{1} \cos θ) R$

$2 \sqrt{\frac{GM}{4 R}} = v_{1} \cos θ$ ……..(1) [by conservation of angular momentum ]

$\frac{1}{2} m (v / 2)^{2} - \frac{{GM}_{e} m}{4 R} = \frac{1}{2} {mv}_{1}^{2} - \frac{{GM}_{1} m}{R}$ ………(2)

$v_{1} = \frac{5}{4} \sqrt{\frac{G M}{R}}$

from (i) $\sqrt{\frac{GM}{R}} = \frac{5}{4} \sqrt{\frac{G M}{R}} \cos θ$

$\cos θ = 4 / 5 \Rightarrow θ = 37^{\circ}$

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE