Three identical ideal springs, each of spring constant K = 2000 N/m are connected in three different arrangements as shown in the figure-I, figure-II and figure-III respectively.

A massless hook A is connected to the lower and of each configuration. If a mass of 10kg is connected to hook A, the magnitude of displacement of point P are `x_(1), x_(2)` and `x_(3)` in figure-I, figure-II and figure-III respectively. Choose the correct option.

Options

A. `x_(1)=0.150m, x_(2)=0.075 m, x_(3)=0.075m`
B. `x_(1)=0.050m, x_(2)=0.025m, x_(3)=0.050m`
C. `x_(1)=0.050m, x_(2)=0.025m, x_(3)=0.025m`
D. `x_(1)=0.025m, x_(2)=0.050m, x_(3)=0.050m`

Answer

B

Explanation

`x_(10)=(3mg)/(k)`
`kx_(1)=(k)/(2)(x_(10)-x_(1))`
`rArr (3kx_(1))/(2)=(k)/(2)x_(10)`
`rArr 3x_(1)=x_(10)`
`rArr x_(10)=(mg)/(k)=0.05m`
`x_(20)=(3mg)/(2k)`
`2kx_(2)=k(x_(20)-x)`
`rArr x_(2)=(x_(20))/(3)=(mg)/(2k)=0.025m`
`x_(30)=(3mg)/(2k)`
`kx_(3)=2k(x_(20)-x_(3))`
`rArr x_(3)=(2x_(20))/(3k)=(mg)/(k)=0.05m`