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ENERGY OF ORBITTING SATELLITES
39.A particle fall towards earth from indinity.The velocity with which it reaches earths surface is --
40.A stone is dropped from a height equal to nR, where R is the radius of the earth,from the surface of the earth.The velocity of the stone on reaching the surface of the earth is----

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Solution

39-
Suppose a particle falls from rest from a point A at a distance d from the centre of the earth. Suppose at time t second, the particle is at a distance x from the centre. At this point the velocity of the particle is v. Then, we have a formula for v:

v2=2gr2[1x-1d]Now, it is given that the particle falls from rest at infinity i.e.d=So, v2=2gr2[1x-1]=2gr2[1x-0]or v2=2gr2xOn the surface of the earth, x=rThus, the velocity of the particle on reaching the earth's surface isv2=2gror v=2gr

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