Home
Class 12
PHYSICS
Distance between the centres of two star...

Distance between the centres of two stars is `10a`. The masses of these stars are `M` and `16 M` and their radit `a` and `2a` respectively. A body of mass `m` is fired straight from the surface of the larger star towards the smaller star. What should be its minimum inital speed to each the surface of the smaller star? Obtain the expression in terms of `G`, `M` and `a`.

Text Solution

Verified by Experts

The correct Answer is:
`3/2`
Let the force of attraction becomes zero at P at a distance r from bigger star.

As this point gravitational field strength becomes zero or at P field due to bigger star is equal and opposite due to smaller star.
`(GM_B)/r^2=(GM_S)/((10a-r)^2) , (16M)/r^2 =M/((10a-r)^2) rArr r=8a`
Now if we fire a mass m from bigger star giving it such a velocity that is sufficient to cross point P, then later on due to more force by the star `M_B` it will pull it towards itself. Now from conservation of mechanical energy of mass m from surface of larger star to point P.
`-(GM_B M)/(2a) - (GM_S M)/(8a) +1/2mv_"min"^2 =(-GM_Bm)/(8a)-(GM_Sm)/(2a) + 0 " " [ because M_B=16M M_S=M]`
After solving we get `v_"min"=3/2sqrt((5GM)/a)`
Promotional Banner

Topper's Solved these Questions

  • GRAVITATION

    VMC MODULES ENGLISH|Exercise JEE Advance (Archive) FILL IN THE BLANKS TYPE|6 Videos

  • GRAVITATION

    VMC MODULES ENGLISH|Exercise JEE Advance (Archive) TRUE/FALSE|1 Videos

  • GRAVITATION

    VMC MODULES ENGLISH|Exercise JEE Advance (Archive)MATCH MATRIX|1 Videos

  • GASEOUS STATE & THERMODYNAMICS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE )|111 Videos

  • INTRODUCTION TO VECTORS & FORCES

    VMC MODULES ENGLISH|Exercise JEE Advanced ( ARCHIVE LEVEL-2)|12 Videos

Similar Questions

Explore conceptually related problems

Distance between the centres of two stars is 10a . The masses of these stars are M and 16 M and their radii a and 2a respectively. A body of mass m is fired straight from the surface of the larger star towards the surface of the smaller star. What should be its minimum initial speed to reach the surface of the smaller star? Obtain the expression in terms of G , M and a.

Distance between the centres of two stars is 10a . The masses of these stars are M and 16 M and their radii a and 2a respectively. A body of mass m is fired straight from the surface of the larger star towards the surface of the smaller star. What should be its minimum initial speed to reach the surface of the smaller star? Obtain the expression in terms of G , M and a .

Distance between the centres of two rings is a. The masses of these rings are M and 4M . A body of mass m is fired straight from the centre of the heavier ring. What should be its minimum initial speed to cross of lighter ring ? The radius of the both ring is R . (Assume a gt gt R ).

Two planets have masses M and 16 M and their radii are a and 2a, respectively. The separation between the centres of the planets is 10a. A body of mass m is fired trom the surface of the larger planet towards the samller planet along the line joining their centres. For the body to be able to reach at the surface of smaller planet, the minimum firing speed needed is :

The distance of centre of mass from point O of two square plates system, as shown,( if masses of plates are 2m and m and their edges are 'a' and '2a' respectively) is

A fixed spherical shell of inner radius R and outer radius 2R has mass M, A particle of mass m is held at rest at a distance 2R from the surface of the body. If the particle is released from that point, with what speed will it hit surface of the spherical body ?

Two homogeneous spheres A and B of masses m and 2m having radii 2a and a respectively are placed in touch . The distance of the centre of mass from the first sphere is

Two planets of mass M and 16M of radius a and 2a respectively, are at distance 10a . Find minimum speed of a particle of mass m at surface of smaller planet so that it can reached from smaller planet to larger planet.

A body of mass 2 kg is dropped from rest from a height 20 m from the surface of Earth. The body hits the ground with velocity 10 m/s, then work done: (g=10m//s^(2))

What impulse need to be given to a body of mass m , released from the surface of earth along a straight tunnel passing through centre of earth, at the centre of earth, to bring it to rest. (Mass of earth M, radius of earth R)