A particle is moving in a circle of radius `r` centred at `O` with constant speed `v`. What is the change in velocity in moving from `A "to" B (/_ AOB = 40^@)` ?

Options

A. ` 2v cos 40^@`
B. `2 v sin 20^@`
C. ` 2v cosec 40^@`
D. ` 2 v sec 20^@`

Answer

B

Explanation

Here, ` |vec A | =| vec _v | = v`
Change in velocity `
` Delta vec v = vec _B - vec v_A = vec v_B + (- verc v_A)`
.
Angle between ` vec v _B` and ` (-vec v_A)`
` = 80^@ - 40^@ = 140^@`
Delta v = sqrt( v^2 +v^2 + 2 v.v cos 14 0^@)`
` = sqrt (v^2 +v^2 + 2 v^2 cos (180^@) - 40^@)`
` = sqrt ( v^2 xx 2 sin ^2 20^@) = 2 v sin 20 .