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 Ts

(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 

Moderate
Solution

(i) Tst=2π(R+h)3GM=2πRg                               As h<R and GM=gR2(ii) Tma=2πRg(iii) Tsp=2π1g1l+1R=2πR2g                     [ As l=R](iv) Tis=2πRg                                                           [ As l=]

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