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. `1.3`
B. `-0.5m`
C. `0.5m`
D. None of these

Answer

B

Explanation

As the springs have natural length initially, if one spring is compressed, the other must be expanded. Hence the compression will be negative.
The free-body diagram of `m_(2)`
`T+F_(2)=80N` and `F_(2)=70xx0.5=35N`
`thereforeT=80-35=45N`
FBD of `m_(1)`
`T+F_(1)=m_(1)g` or `F_(1)=-25N`
`thereforeX_(1)=(-25)/(K_(1))=(-25)/(50)=-0.5m`