MCQ
The radii of circular orbits of two satellites $A$ and $B$ of the earth, are $4R$ and $R,$ respectively. If the speed of satellite $A$ is $3\, V,$ then the speed of satellite $B$ will be ...... $V$
- A$12 $
- ✓$6$
- C$\frac{4}{3}$
- D$\frac{3}{2}$
✓
Answer
Correct option: B.
$6$
b
Orbital speed of the satellite around the earth is $v = \sqrt {\frac{{GM}}{r}} $
Orbital speed of the satellite around the earth is $v = \sqrt {\frac{{GM}}{r}} $
For satellite $A $
${r_A} = 4R,{v_A} = 3V$
${v_A} = \sqrt {\frac{{GM}}{{{r_A}}}} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...(i)$
For satellite $B $
${r_B} = R,{v_B} = ?$
${v_B} = \sqrt {\frac{{GM}}{{{r_B}}}} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( {ii} \right)$
Dividing equation $(ii)$ by equation $(i)$ , we get
$\frac{{{v_B}}}{{{v_A}}} = \sqrt {\frac{{{r_A}}}{{{r_B}}}} \,\,or\,\,{v_B} = {v_A}\sqrt {\frac{{{r_A}}}{{{r_B}}}} $
Substituting the given values, we get
${v_B} = 3V\sqrt {\frac{{4R}}{R}} \,\,or\,\,{v_B} = 6V$
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