The period of a satellite in circcular orbit of radius 12000 km around a planet is 3h. What is the period o a satellite in circular orbit of radius 48000 km around the same planet ?

Options

A. 18 h
B. 14 h
C. 24 h
D. 32 h

Answer

C

Explanation

As ` T prop ( r ) ^ ( 3//2 ) `
If 'T' be the period in an orbit of radius r', then ` ( T ) /( T' ) = (( r ) /( r ' ) ) ^ ( 3//2 ) `
or ` ( 3 )/( T' ) = [ ( 12000 ) /( 48000) ] ^ ( 3//2) = [ ( 1 ) /( 4) ]^ (3//2 ) = ( 1 ) /( 8 ) `
` therefore T' = 24 h `