Question

Figure shows three identical springs A, B, C. when a 4 kg weight is hung on A, it descends by 1 cm. When a 6kg weight is hung on C, it will descend by

• A. 1.5 cm
• B. 3.0 cm
• C. 4.5 cm
• D. 6.0 cm

Answer 1

The correct option is B 3.0 cm

Let k be the force constant of each spring. The force F needed to extend the spring A by an amount x is
$F=kxorx=\frac{F}{k}$
In Fig, the springs are connected in series. Therefore, the force constant k’ of the combination is given by
$\frac{1}{k^{\prime }}=\frac{1}{k}+\frac{1}{k}$
Or k' = $\frac{k}{2}$
If a force F’ is applied, the combination will extend by
$x^{\prime }=\frac{F^{\prime }}{k^{\prime }}$
Thus $\frac{x^{\prime }}{x}$=$\frac{F^{\prime }}{F}.\frac{k}{k^{\prime }}$= $\frac{6}{4}\times \frac{k}{k/2}$=3
Or x' = 3x = $3\times 1cm=3cm$
Hence the correct choice is (b).