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NEET 2010
Exam
NEET
Year
2010
Subject
Physics
Chapter
Gravitation

NEET 2010 · Physics · Gravitation

The radii of circular orbits of two satellites A and B of the earth...

The radii of circular orbits of two satellites A and BB of the earth are 4R4 R and RR, respectively. If the speed of satellite AA is 3v3 v, then the speed of satellite BB will be

Options

  1. A3y/43 y / 4
  2. B6v6 v
  3. C12y12 y
  4. D3v/23 v / 2

Correct answer

B. 6v6 v

Step-by-step solution

 Orbital velocity of satellite v=GMr⇒vAvB=rBrA=R4R=12∴vAvB=3vvB=12∴vB=6v\begin{aligned}& \text{ Orbital velocity of satellite } \mathrm{v}=\sqrt{\frac{\mathrm{GM}}{\mathrm{r}}}\\ & \begin{array}{ll} \Rightarrow& \frac{\mathrm{v}_{\mathrm{A}}}{\mathrm{v}_{\mathrm{B}}}=\sqrt{\frac{\mathrm{r}_{\mathrm{B}}}{\mathrm{r}_{\mathrm{A}}}}=\sqrt{\frac{\mathrm{R}}{4 \mathrm{R}}}=\frac{1}{2}\\ \therefore & \frac{\mathrm{v}_{\mathrm{A}}}{\mathrm{v}_{\mathrm{B}}}=\frac{3 \mathrm{v}}{\mathrm{v}_{\mathrm{B}}}=\frac{1}{2}\\ \therefore & \mathrm{v}_{\mathrm{B}}=6 \mathrm{v} \end{array} \end{aligned}
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