Gravitation

JEE Main level, single correct, medium

212 of 223

Question 212 of 223

The distance between Sun and Earth is RR. The duration of year if the distance between Sun and Earth becomes 3R3R will be :

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Answer: (B) 33yr3\sqrt{3}yr

According to Kepler's Third Law – The Law of Periods,

T2∝R3{T}^{2}\propto {R}^{3}

where TT is time taken by the planet to go once around the sun and RR is the semi-major axis (distance) of the elliptical orbit.

∴T2=kR3…∴{T}^{2}={kR}^{3}\ldots(i)

Where kk is a constant of proportionality.

When RR becomes 33 times, let the time period be (T′)\left({T}^{'}\right).

∴(T′)2=k(3R)3…(ii)∴{\left({T}^{'}\right)}^{2}=k(3R{)}^{3}\ldots (ii)

∴T2(T′)2=127∴\dfrac{{T}^{2}}{{\left({T}^{'}\right)}^{2}}=\dfrac{1}{27}

So, time period will be 33yr3\sqrt{3}yr.

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