A particle moves is X-Y plane under the influence of a force F such that its instantaneous momentum is P = i2 cos t + j2 sin t, what is the angle between the force and instantaneous momentum?

Question

A particle moves is X-Y plane under the influence of a force F such that its instantaneous momentum is P = i2 cos t + j2 sin t, what is the angle between the force and instantaneous momentum? (A)  0°  (B)  180°  (C)  90°  (D)  45°

Tardigrade Admin · Accepted Answer

Here, p = i2 cos t + j2 cos t F (d p/d t)=-2 i sin t+2 j cos t F ⋅ P=(-2 i sin t+2 j cos t) ⋅(2 i cos t+j sin t) =-4 sin t cos t=+4 sin t cos t=0 Therefore, θ=90°

Q. A particle moves is $X - Y$ plane under the influence of a force $F$ such that its instantaneous momentum is $P = i^{2} cos t + j^{2} sin t$ , what is the angle between the force and instantaneous momentum?

$0^{\circ}$

$18 0^{\circ}$

$9 0^{\circ}$

$4 5^{\circ}$

Here, $p = i^{2} cos t + j^{2} cos t$
$F \frac{d p}{d t} = - 2 i sin t + 2 j cos t$
$F \cdot P = (- 2 i sin t + 2 j cos t) \cdot (2 i cos t + j sin t)$
$= - 4 sin t cos t = + 4 sin t cos t = 0$
Therefore, $θ = 9 0^{\circ}$

Q. A particle moves is X−Y plane under the influence of a force F such that its instantaneous momentum is P=i2cost+j2sint, what is the angle between the force and instantaneous momentum?

0∘

180∘

90∘

45∘