A satellite is launched into a circular orbit of radius ' R '...

A satellite is launched into a circular orbit of radius ' R ' around the earth. A second satellite 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

Options

A $9 \%$
B $3 \%$
C $4.5 \%$
D $2.5 \%$

Correct answer

C. $4.5 \%$

Step-by-step solution

T_1 \propto(R)^{3 / 2}

and

T_2 \propto(1.03 R)^{3 / 2}

\Rightarrow \quad T_2=(1.03 R)^{3 / 2} \cdot T_1 \approx 1.045 T_1

T_2

will larger by

4.5 \%

w.r.t.

T_1

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