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An object is moving in the x-y plane wit...

An object is moving in the x-y plane with the position as a function of time given by `vecr = x(t)hati + y(t)hatj`. Point O is at `x = 0 , y = 0` . The object is definitely moving towards O when

A

`v_xgt0,v_ygt0`

B

`v_xlt0,v_ylt0`

C

`xv_x+yv_ylt0`

D

`xv_x+yv_ygt0`

Text Solution

Verified by Experts

The correct Answer is:
C
c. `vecr = xhati + yhatj`
`vec v = (dvecr)/(dt) = (dx)/(dt) hati +(dy)/(dt)hatj = v_xhati + y_(y)hatj`
If `vecr` and `vecv` are in opposite directions, then definitely the
particle will be moving towards origin O, for this `vecr*vecv lt0`
`rArr xv_x + yv_y lt0` .
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