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A particle moves in the xy-plane under t...

A particle moves in the xy-plane under the action of a force F such that the components of its linear momentum p at any time t are `p_(x)=2cost`, `p_(y)=2sint`. The angle between F and p at time t is

A

`90^(@)`

B

`0^(@)`

C

`180^(@)`

D

`30^(@)`

Text Solution

Verified by Experts

The correct Answer is:
A
`vec(p) p_(x)hat(i) + p_(y)hat(j) = 2cos t hat(i) + 2 sin t hat(j)`
`vec(F) = (dvec(p))/(dt) = -2 sin t hat(i) + 2cos t hat(j)`
`vec(F).vec(p) = 0" " i.e. theta = 90^(@)`
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