18. A particle moves in the XY plane under the action of a force F such that the value of
linear momentum (p) at any time is px=2 cost,
Py=2sint. The angle o between F and p at a
given time 't' will be

Answer t= 90°

explantion: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°

unbalanced force

explanation: