An artificial satellite is revolving round the earth. The radius of its circular orbit is half the orbital radius of moon. The time taken by this satellite in completing one revolution will be

2

lunar months.

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2^{- 2 / 3}

lunar months.

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2^{- 3 / 2}

lunar months.

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1 / 2

lunar months.

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Solution

The correct option is D $2^{- 3 / 2}$ lunar months.
Using Kepler's $3$ rd law, for moon $T^{2} = a^{3}$
for satellite, $(T^{'})^{2} = (a^{'})^{3} = {(\frac{a}{2})}^{3} = \frac{T^{2}}{2^{3}}$
$T^{'} = (2)^{- 3 / 2} T = (2)^{- 3 / 2}$ lunar month.
where $T =$ lunar month , time between two identical new moons or full moons.

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An artificial satellite is revolving round the earth. The radius of its circular orbit is half the orbital radius of moon. The time taken by this satellite in completing one revolution will be

The correct option is D 2−3/2 lunar months.Using Kepler's 3rd law, for moon T2=a3 for satellite, (T′)2=(a′)3=(a2)3=T223T′=(2)−3/2T=(2)−3/2 lunar month. where T= lunar month , time between two identical new moons or full moons.