Two small satellites are moving in circular orbits around the earth at a distance R and `R + Delta R` from the centre of the earth. If their time period of rotation are T and `T + Delta T ` respectively, then

Options

A. `Delta T = T (DeltaR)/(R )`
B. `Delta T = 3T (DeltaR)/(R )`
C. `Delta = (3)/(2) T (DeltaR )/(R )`
D. `Delta T = (2)/(3) T (DeltaR )/(R )`

Answer

C

Explanation

`T prop R^((3)/(2))`
`((T + DeltaT))/(T ) = ((R + DeltaR )/(R ))^(3//2)`
`1+ (Delta T)/(T ) = (1+ (DeltaR )/(R ))^(3//2)`
`:. Delta R lt lt R `
`1 + (Delta T)/(T ) = 1 + (3)/(2) (DeltaR )/(R )`
`(Delta T)/(T ) = (3)/(2) (Delta R )/(R )`
`Delta T = (3)/(2) T . (DeltaR) /(R)`