First slide
Motion of planets and satellites
Question

In the following four Periods,
(i) Time of revolution of a satellite just above the earth's surface Tst
(ii) Period of oscillation of mass inside the tunnel bored along the diameter of the earth Tma
(iii) Period of simple pendulum having a length equal to the earth's radius in a uniform field of 9.8 N/kg Tsp
(iv) Period of an infinite length simple pendulum in the earth's real gravitational field Tis

Difficult
Solution

(i) Tst=2π(R+h)3GM=2πRg

 [As h<<R and GM=gR2

 (ii) Tma=2πRg

 (iii) Tsp=2π1g1l+lR=2πR2g

[ As l=R]

 (iv) Tis=2πRg[ As l=]

 

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