Initially a satellite of 100 kg is in a circular orbit of radius $1.5 \mathrm{R}_{\mathrm{E}}$. This satellite can be moved to a circular orbit of radius $3 \mathrm{R}_{\mathrm{E}}$ by supplying $\alpha \times 10^{6} \mathrm{~J}$ of energy. The value of $\alpha$ is ______. (Take Radius of Earth $\mathrm{R}_{\mathrm{E}}=6 \times 10^{6} \mathrm{~m}$ and $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$)

JEE Main · 2026 · 21 Jan 2026 · Shift 1 · Gravitation

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✓ Correct

Answer: (D)

Solution

A circular orbit has total energy

E = - \frac{G M _{E} m}{2 r}

, so the energy needed to raise it is

Δ E = \frac{G M _{E} m}{2 R _{E}} (\frac{1}{1.5} - \frac{1}{3}) = \frac{G M _{E} m}{6 R _{E}}

. Using

\frac{G M _{E}}{R _{E}} = g R_{E}

, this becomes

\frac{g m R _{E}}{6} = \frac{10 \times 100 \times 6 \times 1 0 ^{6}}{6} = 1000 \times 1 0^{6} J

, so

α = 1000

JEE Main · 2026 · 21 Jan 2026 · Shift 1 · Single correct option

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