Book Online Demo

Check Your IQ

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

Q.

Two uniform solid spheres of equal radii R, but mass M and 4M have a centre to centre separation is 6R as shown in fig.
The spheres are held fixed. A projectile of mass m projected with minimum velocity from the surface of sphere directly towards the centre of the second sphere so that reaches the surface of the second sphere. If the speed with which projectile reaches the surface of the sphere of mass 4M is $3 \sqrt{\frac{xGM}{5 R}} find x$

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

answer is 3.

(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

null point between the two masses is $\frac{6 R}{\sqrt{\frac{4 M}{M} + 1}} = 2 R$
From null point to the surface of heavy sphere apply law of conservation of energy
$\frac{- GMm}{2 R} - \frac{G 4 Mm}{4 R} = \frac{- GMm}{5 R} - \frac{G 4 Mm}{R} + \frac{1}{2} {mv}^{2}$
$\Rightarrow \frac{- 3 GM}{2 R} = \frac{- 21 GM}{5 R} + \frac{1}{2} V^{2} \Rightarrow \frac{V^{2}}{2} = \frac{27 GM}{10 R} \Rightarrow V = 3 \sqrt{\frac{3 GM}{5 R}}$

Watch 3-min video & get full concept clarity

Related Blogs

Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation

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

JEE

NEET

NEET

Foundation JEE

Foundation JEE

Foundation NEET

Foundation NEET

CBSE

CBSE

Get Expert Academic Guidance – Connect with a Counselor Today!

Related Blogs

Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation

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

Not sure what to do in the future? Don’t worry! We have a FREE career guidance session just for you!

Two uniform solid spheres of equal radii R, but mass M and 4M have a centre to centre separation is 6R as shown in fig.The spheres are held fixed. A projectile of mass m projected with minimum velocity from the surface of sphere directly towards the centre of the second sphere so that reaches the surface of the second sphere. If the speed with which projectile reaches the surface of the sphere of mass 4M is 3xGM5R find x