The system shown in fig is in equilibrium . Masses `m_(1) and m_(2)` are 2kg and 8kg, Respectively. Spring constants `k_(1) and k_(2)` ro `50Nm^(-1) and 70Nm^(-1)`, respectively. If the compression in second spring is 0.5m. What is the compression in first spring?

Options

A. `1.3m`
B. `-0.5m`
C. `0.5m`
D. `0.9m`

Explanation

As the springs are fixed to the horizontal and have the same natural length, hence if one spring is compressed, the other must be expanded. Hence, the compression will be negative.
`F.B.D` of `m_(2)` `T+F_(2)=80N`
and `F_(2)=70xx0.5=35N`
`:. T=80-35=45N`
`F.B.D` of `m_(1)`
`T+F_(1)=mg`
or `45+F_(1)=mg`
`rArr F_(1)= -45+20= -25N`
`:. x_(1)=(-25)/(50)=-0.5m`
`:. ` Compression in first spring `= -0.5m`