Q: A particle moves in the x – y plane under the influence of a force such that its linear momentum is $ \displaystyle \vec{p(t)}= A[\hat{i}\, coskt – \hat{j}\, sinkt] $ where A and k are constants. The angle between the force and momentum is

(a) 0°

(b) 30°

(c) 45°

(d) 90°

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Ans: (d)

Sol: $ \displaystyle \vec{F} = \frac{\vec{dp}}{dt} = A k[-\hat{i}\, sinkt – \hat{j} \, coskt] $

Since , $ \displaystyle \vec{F}.\vec{p} = 0 $

θ = 90°