Two particles are in SHM along same line. Time period of each is `T` and amplitude is `A`. After how much time will they collide if at time `t = 0`. (a) first particle is at `x_(1) = + (A)/(2)` and moving towards positive x - axis and second particle is at `x_(2) = - (A)/(sqrt2)` and moving towards negative x - axis, (b) rest information are same as mentioned in part (a) except that particle first is also moving towards negative x - axis.

Answer

A, B, D

Explanation

(a) `theta_(0) = omega_(1) t + omega_(2) t`

but `omega_(1) = omega_(2) = (2pi)/(T)`
and `theta_(0) = pi + (pi)/(3) + (pi)/(4) = (19)/(12)pi`
`:. (19pi)/(12) = (2pi)/(T)t + (2pi)/(T)t`
or `t = (19)/(48)T`
(b) `theta = 2pi - theta_(0) = 2pi - (19)/(12)pi = (5pi)/(12)`

Two particles will collide when line XX' becomes the line of bisector of angle `theta`.
`:.` Any one of the particle (say - 2) has rotated an angle
`omega t = pi//4 + theta//2`
or `(2pi)/(T) t = (pi)/(4) + (5pi)/(24) = (11pi)/(24)`
`:. t = (11T)/(48)`