JEE Main · 2019 · 12 Jan 2019 · Shift 2 · Gravitation

Two satellites,

A

and

B

, have masses

m

and

2 m

respectively.

A

is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies,

T_{A} / T_{B}

, is :

(A) $\frac{1}{2}$
(B)1✓ Correct
(C)2
(D) $\frac{1}{2}$

Answer: (B)

Solution

A satellite in a circular orbit has kinetic energy

\frac{GM m}{2 r}

. For

A

of mass

m

at radius

R

T_{A} = \frac{GM m}{2 R}

; for

B

of mass

2 m

at radius

2 R

T_{B} = \frac{GM ( 2 m )}{2 ( 2 R )} = \frac{GM m}{2 R}

. The two are equal, so

\frac{T _{A}}{T _{B}} = 1

JEE Main · 2019 · 12 Jan 2019 · Shift 2 · Single correct option

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