i)Derive an expression for critical velocityof satellite.

1.	i)Derive an expression for critical velocityof satellite.
Answer» Consider a satellite of mass m revolving round the Earth at a, height 'h' above the surface of the Earth. Let M be the mass and R be the radius of the Earth. The satellite is moving with velocity V and the radius of the circular orbit isr=R+hr=R+h. Centripetal force = Gravitational force ∴Mv2cr=GMmr2∴Mvc2r=GMmr2 ∴v2c=GMr∴vc2=GMr ∴vc=√GMR+h∴vc=GMR+h This is the expression for critical velocity of a satellite moving in a circular orbit around the Earth, We know that, gh=GM(R+h)2gh=GM(R+h)2 GM=gh(R+h)2GM=gh(R+h)2 Substituting in equation (1), we get ∴vc=√gh(R+h)2R+h∴vc=gh(R+h)2R+h ∴vc=√gh(R+h)∴vc=gh(R+h) whereghghis the acceleration due to gravity at a height above the surface of the Earth.

Answer»

Consider a satellite of mass m revolving round the Earth at a, height 'h' above the surface of the Earth.

Let M be the mass and R be the radius of the Earth.

The satellite is moving with velocity V and the radius of the circular orbit isr=R+hr=R+h. Centripetal force = Gravitational force

∴Mv2cr=GMmr2∴Mvc2r=GMmr2

∴v2c=GMr∴vc2=GMr

∴vc=√GMR+h∴vc=GMR+h

This is the expression for critical velocity of a satellite moving in a circular orbit around the Earth,

We know that,

gh=GM(R+h)2gh=GM(R+h)2

GM=gh(R+h)2GM=gh(R+h)2

Substituting in equation (1), we get

∴vc=√gh(R+h)2R+h∴vc=gh(R+h)2R+h

∴vc=√gh(R+h)∴vc=gh(R+h)

whereghghis the acceleration due to gravity at a height above the surface of the Earth.

Discussion

No Comment Found

Related InterviewSolutions

7. A body has a weight 50 N in air. Afterimmersing completely in liquid its weight is20 N. Then, the buoyant force on the bodywill be
Name the particulate which causes the disease mentioned below:(a)minamata (b)silicosis.
- Where does a body weight more at the surface of the carth or in a mine?
DelyAbody79entire chainthe ch.57. A body of mass 50gm collides elastically with anotherbody of mass 30 gm at rest. Then the percentage lossof the velocity of the colliding body during collision is1) 25% 2) 75% 3) 50% 4) 67%3) 120380.beide
What will be the acceleration of a body of mass5 kg if a force of 200 N is applied on it?
Rig. 5.168.13 Two bodles of masses 10 kg and 20 kg respectively kept on a smooth, hortzontalsurface are tied to the ends of a light string a horizontal force F 600 Nsapplied to lu A (t) B along the direction of string. What is the tension in thestring in each case
culate the gravitational force befween two protons kept at a distance67 x 10-27 kg. (1 femtometre = 10-15 m)
15. A uniform chain of length 2 m is kept on atable such that a length of 60 cm hangs freelyfrom the edge of the table. The total mass ofthe chain is 4 kg. What is the work done inpulling the entire chain onto the table ?(g = 10 m/s)1) 7.2J273.63) 120J4) 1200
Two block of mass 3 kg and 6 kg respectively are placed on a smooth 1.0 m/shorizontal surface. They are connected by a light spring of force 3 kgconstant k 200 N/m. Initially the spring is unstretched. The indicatedzmvelocities are imparted to the blocks. The maximum extension of thespring will be:A30 cm(C) 20 cm2.0 mls(B) 25 cm(D) 15 cm
88. A piece of stone is thrown vertically upwards. It reaches the maximum height in 3 seconds. If the accelerationof the stone be 9.8 m/s directed towards the ground, calculate the initial velocity of the stone with which itis thrown upwards.