A particle is moving on circular path as shown in the figure. Then displacement from `P_1" to " P_2` is 

Options

A. `2 r cos (theta)/2`
B. `2 r tan (theta)/2`
C. `2 r sin theta`
D. `2 r sin (theta)/2`

Answer

D

Explanation

According to cosine formula
`cos theta=(r^2+r^2-x^2)/(2r^2)`
or `2r^(2) cos theta = r^(2) + r^(2) -x^(2)`
or `x^(2)= 2r^(2) - 2r^(2) cos theta = 2r^(2) [1- costheta] = 2r^(2) [ 2sin^(2) ""(theta)/2]`
Displacement from `P_(1) " to " P_(2) ` is ` x = 2r sin(theta)/2`