Home
Class 12
PHYSICS
Two satellites of same mass are launched...

Two satellites of same mass are launched in the same orbit round the earth so as to rotate opposite to each other. They soon collide inelastically and stick together as wreckage. Obtain the total energy of the system before and just after the collision. Describe the subsequent motion of the wreckage.

Text Solution

Verified by Experts

Potential energy of the satellite in its orbit `=-(GMm)/(r )`
`implies K.E.=(|U|)/(2)=(GMm)/(2r)` where `m` is mass of satellite, `M` the mass of the earth and `r` the orbital radius.
Total energy `=K.E.+P.E.`
`=(GMm)/(2r)-(GMm)/(r )=-(GMm)/(2r)`
For two satellites `E=-(GMm)/(r )`
Let v. be the velocity after collision.
By conservation of momentum
`mvecv_(1)+mvecv_(2)=0=(m+m)v.impliesv.=0`
The wreckage of mass `(2m)` has no kinetic energy, but it has only potential energy . So, energy after collision `=-(GM(2m))/(r )`
Therefore, the wreckage falls down under gravity.
Promotional Banner

Topper's Solved these Questions

  • GRAVITATION

    FIITJEE|Exercise Solved problem (Objective)|15 Videos

  • GRAVITATION

    FIITJEE|Exercise Comprehension|13 Videos

  • GRAVITATION

    FIITJEE|Exercise Numerical based Question|2 Videos

  • GMP ASSESMENT

    FIITJEE|Exercise Numerical Based|61 Videos

  • HEAT AND TEMPERATURE

    FIITJEE|Exercise NUMERICAL BASES QUESTIONS|1 Videos

Similar Questions

Explore conceptually related problems

Two identical satellite are kept in the same orbit around the earth to move in opposite directions. If they collide and stick together after some time

Two oppositely rotating satellities of same are launched in the same orbit round the earth. The collide idealistically. What is the ratio of gravitational potential energy before and after collistion?

Two satellites of same mass are orbiting round the earth at heights of r_1 and r_2 from the centre of earth. Their kinetic energies are in the ratio of :

Two satellites of same mass m are revolving round of earth (mass M) in the same orbit of radius r. Rotational directions of the two are opposite therefore, they can collide. Total mechanical energy of the system (both satallites and earths) is (m lt lt M) :-

Consider two satellites A and B of equal mass m, moving in the same circular orbit of radius r around the earth E but in opposite sense of rotation and therefore on a collision course (see figure) (i). In terms of G,M_(e) m and r find the total mechanical energy E_(A)+E_(B) of the two satellite plus earth system before collision (ii). If the collision is completely inelastic so that wreckage remains as one piece of tangled material (mass=2m) find the total mechanical energy immediately after collision. (iii). Describe the subsequent motion of the wreckage.

A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be:

Consider two satellites A and B of equal mass, moving in the same circular orbit of radius r around the earth but in the opposite sense and therefore a collision occurs. (a) Find the total mechanical energy E_(A) + E_(B) of the two satellite-plus-earth system before collision. (b) If the collision is completely inelastic, find the total mechanical energy immediately after collision. Describe the subsequent motion of the combined satellite.