Question

A satellite is launched into a circular orbit of radius 'R' around the earth. A second statellite is launched into an orbit of radius 1.03 R. The time period of revolution of the second satellite is larger than the first one approximately by :-

(1) \(3 \ \%\)

(2) \(4.5 \ \%\)

(3) \(9 \ \%\)

(4) \(2.5\ \%\)

Answer 1

Correct option is : (2) \(4.5 \ \%\) 

\(\mathrm{T}^{2}=\mathrm{KR}^{3}\)

\( \frac{2 \Delta \mathrm{T}}{\mathrm{~T}}=\frac{3 \Delta \mathrm{R}}{\mathrm{R}}\)

\(\frac{2 \Delta \mathrm{T}}{\mathrm{~T}}=\frac{3 \times 0.03 \mathrm{R}}{\mathrm{R}}\)

\(\frac{\Delta \mathrm{T}}{\mathrm{T}}=\frac{3 \times 0.03}{2} \times 100=4.5 \%\)