A particle P of mass 2kg describes an elliptical orbit of semi-major axis $a = 5 m$ and semi-minor axis b =4m due to an attractive force $\frac{λ}{r^{2}}$ towards a focus S where r is the distance of P from S and $λ = 40 N m^{2}, N o w,$

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Its velocity at C is $2 m s^{- 1}$

Its velocity at A is $1 m s^{- 1}$

Its velocity at A is $4 m s^{- 1}$

answer is D.

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Detailed Solution

$F = \frac{- d u}{d r} = \frac{λ}{r^{2}}$
Eccentricity $e = \sqrt{1 - \frac{b^{2}}{a^{2}}} = \frac{3}{5}$

SO = 3m, SA= 2m, SC = 8m
$U_{A} = - \frac{λ}{2} = - 20 J, U_{c} = - 5 J$

$r_{A} m V_{A} = r_{c} m V_{c}$

$2 V_{A} = 8 V_{c}$ , $\frac{1}{2} m v_{A}^{2} - 20 = \frac{1}{2} m v_{c}^{2} - 5$ ,
Solving we get $V_{A} = 4 m / s$

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