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 $λ = 40 N m^{2}, N o w,$

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

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.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

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 $V_{A} = 4 m / s$

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE