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Units And Measurement

Question
CBSEENPH11017763

A body is moving under radial force in an elliptical orbit. The farthest position of body from the source of force is twice as that of nearest position. If the velocity of body at farthest point is 20m/s, then find the velocity of body at nearest point.

Solution
The radial force exerts zero torque on the body.
Therefore angular momentum of body will remain conserve,

straight i. straight e. comma space space space space straight m subscript 1 straight v subscript 1 straight r subscript 1 equals straight m subscript 2 straight v subscript 2 straight r subscript 2 space end subscript

rightwards double arrow space space space space space space space space space space space space space space straight v subscript 2 equals fraction numerator straight v subscript 1 straight r subscript 1 over denominator straight r subscript 2 end fraction
H e r e comma space space

straight r subscript 1 equals 2 straight r subscript 2 comma space

straight v subscript 1 equals 20 space straight m divided by straight s space

straight v subscript 2 equals fraction numerator 20 cross times 2 straight r subscript 2 over denominator straight r subscript 2 end fraction

space space space equals 40 space straight m divided by straight s