Physics - NLM Question with Solution | TestHub

Parallel: k_1 + k_2 = 250 N/m.

$${\mathrm{k}}_1+{\mathrm{k}}_2=250$$

Series:

$$\frac{{\mathrm{k}}_1{\mathrm{k}}_2}{{\mathrm{k}}_1+{\mathrm{k}}_2}=60\Rightarrow {\mathrm{k}}_1{\mathrm{k}}_2=60\times 250=15000$$

So k_1, k_2 are roots of

$${\mathrm{x}}^2-250\mathrm{x}+15000=0$$

$$\mathrm{x}=\frac{250\pm \sqrt{250^2-4\times 15000}}{2}=\frac{250\pm 50}{2}=150,100$$

The spring constants are 100 N/m and 150 N/m. Correct option: (3).