A particle is describing uniform circular motion in the anti-clockwise sense such that its time period of revolution is T. At t = 0 the particle is observed to be at A. If `theta_1` be the angle
between acceleration vector at `t=T/4` and average velocity vector in the time interval 0 to T/4 and `theta_2` be the angle between acceleration vector at `t= T/4` and the vector representing change in velocity in the time interval 0 to T/4, then :

Options

A. `theta_1 = 135^@ , theta_2 = 45^@`
B. `theta_1 = 135^@ , theta_2 = 135^@`
C. `theta_1 = 45^@, theta _2 = 135^@`
D. `theta _1 = 45^@ , theta_2 = 45^@`

Answer

A

Explanation

Let initial point A is on –y-axis and at t =T/4, it is at + x-axis.
At `t =T//4, ...…(i)`
` At t=0, overset(-)V=V hati, at t=T//4, overset(-)V=Vhatj`
`triangleoverset(-)V=Vhatj-Vhati …(ii)`
Average velocity from t=0 to `t=T//4" is equal to "(R hati-(-R hatj))/(T//4)=(4R)/(T)=(hati+hatj) …(iii)`
`rArr theta_(1)` = angle between vectors `-hati and hati+hatj=135^(@) and theta_(2)` =angle between vector `-hati and hatj-hati=45^(@)`