AI Mentor

Check Your IQ

Free Expert Demo

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

Two hypothetical planets of masses $m_{1}$ and $m_{2}$ are at rest when they are infinite distance apart. Because of the gravitational force they move towards each other along the line joining their centres.
What is their speed when their separation is ‘d’?
(Speed of $m_{1}$ is $v_{1}$ and that of $m_{2}$ is $v_{2}$ )

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$v_{1} = v_{2_{}}$

$v_{1} = m_{2} \sqrt{\frac{2 G}{d (m_{1} + m_{2})}}, v_{2} = m_{1} \sqrt{\frac{2 G}{d (m_{1} + m_{2})}}$

$v_{1} = m_{1} \sqrt{\frac{2 G}{d (m_{1} + m_{2})}}, v_{2} = m_{2} \sqrt{\frac{2 G}{d (m_{1} + m_{2})}}$

$v_{1} = m_{2} \sqrt{\frac{2 G}{m_{1}}}, v_{2} = m_{2} \sqrt{\frac{2 G}{m_{2}}}$

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

We choose reference point, infinity, where total energy of the system is zero.
So,

From conservation of energy,

0= $\frac{1}{2} m_{1} v_{1}^{2} + \frac{1}{2} m_{2} v_{2}^{2} - \frac{G m_{1} m_{2}}{d}$

and conservation of linear momentum,

$m_{1} v_{1} + m_{2} v_{2} = 0$ , we get the values of velocities

$v_{1} = m_{2} \sqrt{\frac{2 G}{d (m_{1} + m_{2})}}, and, v_{2} = m_{1} \sqrt{\frac{2 G}{d (m_{1} + m_{2})}}$

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

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

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!