Question

A particle moves in the x-y plane under the action of the force F such that
the value of it's linear momentum p at any time t is p(x)= 2 cost and pſy) =2 sint
. The angle between F and p at a given time t will be​

Answer 1

Answer:

Force is defined as the rate of change of momentum.

P

x

=2cost

P

y

=2sint

P

=2cost

i

^

+2sint

j

^

F=

dt

dP

F

x

=−2sint

F

y

=2cost

From law of vector dot product,

A

.

B

=ABcosθ

Where θ is angle between them.

cosθ=

AB

A

.

B

Here,

cosθ=

FP

F

.

P

cosθ=

FP

−2cost×2sint+2cost+2sint

cosθ=0

θ=90°