JEE Main 2026 — Jan 21, Shift 1 — Physics solution

JEE Main2026Jan 21, Shift 1Physics

Initially a satellite of 100 kg is in a circular orbit of radius $1.5 R_{E}$ . This satellite can be moved to a circular orbit of radius $3 R_{E}$ by supplying $α \times 1 0^{6}$ J of energy. The value of $α$ is __________.

(Take Radius of Earth $R_{E} = 6 \times 1 0^{6}$ m and g = 10 m/s $^{2}$ )

A
150
B
500
C
100
D
1000

Solution

Total energy of a satellite in a circular orbit of radius $r$ : $E = - \frac{GM m}{2 r}$ .

Energy needed: $Δ E = E_{f} - E_{i} = - \frac{GM m}{2} (\frac{1}{3 R _{E}} - \frac{1}{1.5 R _{E}}) = \frac{GM m}{6 R _{E}}$ .

Use $g = GM / R_{E}^{2} \Rightarrow GM / R_{E} = g R_{E}$ , so $Δ E = \frac{g m R _{E}}{6} = \frac{10 \times 100 \times 6 \times 1 0 ^{6}}{6} = 1 0^{9}$ J $= 1000 \times 1 0^{6}$ J.

Therefore $α = 1000$ .

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