Find the time period of the motion of the particle shown in figure. Neglected small effect of the bend near the bottom.

Answer

C

Explanation

Let the time taken to travel AB and BC be `t_1 and t_2` respectively.
For part `AB, a_1=gsin45^@`
`s_1=0.1/(sin45^@)=2m`
Let `v=velocity t B `
`:.v^2-u^2=2a_1s_1`
`rarr v^2=2xxgsin45^@xx0.1/(sin45^@)`
=2
`rarr v=sqrt2 m/s`
`:. t_1=(v-u)/a_1=sqrt(2-0)/(g/sqrt2)`
`=2/g=2/10=0.2sec`......A
Agasin for part BC
`a_2=gsin60^@`
`u=sqrt2v=0`
`:. t_2=(0-sqrt2)/(g/(3sqrt2))=(2sqrt2)/(sqrt3g)`
`=(2xx(1.414))/((1.732)xx10)=0.165sec`
So time period `=2(t_1+t_2)`
`=2(0.2+0.155)=0.73sec`