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Question

Figure shows the orbit of a planet P round the sun S. AB and CD are the minor and major axes of the ellipse. If t1 is the time taken by the planet to travel along ACB and t2 the time along BDA, then :
126528_fe20af8d217a4e478560457970fddb68.png

A
t1=t2
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B
t1>t2
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C
t1<t2
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D
nothing can be concluded
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Solution

The correct option is B t1>t2
Here, the angular momentum is conserved i.e. mvr is constant. Where r is the distance from center of the sun to center of the planet.

Now, consider one point each from both the mentioned paths.(Shown in fig.)

Applying conservation of angular momentum for these points we get

mv1r1=mv2r2 . Simplifying this, v1v2=r2r1<1

Time period are given by

t1=Lv1,t2=Lv2

Comparing them by taking the ratio

t1t2=Lv1×v2L

So, t1t2=v2v1>1.Thus t1>t2

236137_126528_ans_da31469e604b4ae29c381c3d5194d28b.png

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