Question

A particle moves in the x-y plane under the action of a force `vec"F"` such that the value of its linear momentum `(vec"p")` at any time t is P_x = 2 cos t, p_y = 2 sin t. The angle `theta`  between `vec"F"` and `vec"P"` at a given time twill be ____________.

विकल्प

• 0°

• 30°

• 90°

• 180°

Answer 1

A particle moves in the x-y plane under the action of a force `vec"F"` such that the value of its linear momentum `(vec"p")` at any time t is P_x = 2 cos t, p_y = 2 sin t. The angle `theta`  between `vec"F"` and `vec"P"` at a given time twill be 90°.

Explanation:

P_x = 2 cos t, P_y= 2 sin t

`therefore  vec"P" = 2 "cos t"  hati + 2  "sin t"  hatj`

`vec"F" = vec("dp")/"dt" = -2  "sin t"  hati + 2  "cos t"  hatj`

`vec"F" * vec"P" = (-2 "sin t"  hati + 2  "cos t"  hatj) (2 "sin t"  hati + 2  "cos t"  hatj)`

`vec"F" * vec"P" = 0`

`therefore theta = 90°`