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`

Answer

B

Explanation

As the spring 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)=70 xx 0.5 = 35 N`
`:. T=80-35 = 45 N`
FBD of `m_(1)`
`T+F_(1)=m_(1)g or F_(1)=-25N`
`:. X_(1)=(-25)/(k_(1))=(-25)/(50)= -0.5 m`.
Therefore, compression in first spring is `-0.5 m`.
(negative sign indicates that it is extension)