A tunnel is dug along the diameter of earth. There is a particle of mass m at centre of tunnel. Find minimum velocity given to the particle so that it just reaches the surface of earth (R=radius of earth, M= mass of earth)

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

$\sqrt{\frac{G M}{R}}$

$\sqrt{\frac{G M}{2 R}}$

$\sqrt{\frac{2 G M}{R}}$

$\sqrt{\frac{3 G M}{R}}$

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

At center of earth, total energy
$E_{1} = \frac{1}{2} m V^{2} - \frac{3 G M m}{2 R}$
If particle reach surface of earth V=0, total energy
$E_{2} = 0 - \frac{G M m}{R}$
Apply LCME
$V = \sqrt{\frac{G M}{R}}$ .

Watch 3-min video & get full concept clarity

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

How to Join IIT after 10th

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

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

How to Join IIT after 10th