A small body of mass ‘ $m$ ’ is projected from the surface of a given planet as shown in the figure. If small body has velocity which is just sufficient to get out from the gravity of planet then time taken by small body to reach at height of $3 R$ from the surface of planet is $K \sqrt{\frac{2 R^{3}}{G M}}$ . Find the value of $K$

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

answer is 2.33.

(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

Speed of projection $(v_{0}) = \sqrt{\frac{2 G M}{R}}$

$\frac{1}{2} m v^{2} - \frac{G M m}{R} = \frac{1}{2} m v^{2} - \frac{G M m}{r} v = \sqrt{\frac{2 G M}{r}} \int_{R}^{4 R} \sqrt{r} d r = \sqrt{2 G M} \int_{0}^{t} d t t = \frac{7}{3} \sqrt{\frac{2 R^{3}}{G M}}$

Watch 3-min video & get full concept clarity

tricks from toppers of Infinity Learn

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET