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Q.

A particle P of mass 2kg describes an elliptical orbit of semi-major axis  a=5m and semi-minor axisb=4m   due to an attractive force λr2 towards a focus S where r is the distance of P from S and  λ=40Nm2. Now, 

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a

Its velocity at A is 2m/s

b

Its velocity at A is 3m/s 

c

Its velocity at A is 1m/s 

d

Its velocity at A is 4m/s

answer is D.

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Detailed Solution

F=dudr=λr2

Eccentricity    e=1b2a2=35                                  U=λr
So, SO = 3m; SA = 2m;  SC = 8m
UA=λ2=20J;Uc=5J
rAmVA=rcmVc
2VA=8Vc
Also,  12mVr220=12mVc25
Solving we get  VA=4m/s
 

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