Gravitation | JEE Main previous year questions with Solutions

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Topic Question Set

Q 1 :
Two satellite A and B go round a planet in circular orbits having radii 4R and R respectively. If the speed of A is 3v, the speed of B will be [2024]

$6 v$
$12 v$
$\frac{4}{3} v$
$3 v$

1

2

3

4

(A)

Q 2 :
A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is

(Given = Radius of geo-stationary orbit for earth is $4.2 \times 10^{4}$ km) [2024]

$1.05 \times 10^{4}$ km
$1.4 \times 10^{4}$ km
$1.68 \times 10^{5}$ km
$8.4 \times 10^{4}$ km

1

2

3

4

(A) By Kepler's law, $T^{2} = \frac{4 π^{2} R^{3}}{G M} \Rightarrow T^{2} \propto \frac{R^{3}}{M}$

${(\frac{T_{1}}{T_{2}})}^{2} = {(\frac{R_{1}}{R_{2}})}^{3} (\frac{M_{2}}{M_{1}})$

${(\frac{24}{6})}^{2} = {(\frac{4.2 \times 10^{4}}{R_{2}})}^{3} \times (\frac{\frac{M_{E}}{4}}{M_{E}})$

$4^{2} \times 4 = {(\frac{4.2 \times 10^{4}}{R_{2}})}^{3} \Rightarrow R_{2} = 1.05 \times 10^{4}$ km

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