question_answer

Two identical springs are attached to a small block\[p\]. The other ends of the springs are fixed at \[A\] and\[B\]. When \[p\]the extension of top spring is in equilibrium is 20 cm and extension p of bottom spring is 10 cm. The period of small vertical oscillations of? about its equilibrium position is (use \[g=9.8\,m/{{s}^{2}}\])

A) \[\frac{2\pi }{7}\sec \]               

B) \[\frac{\pi }{7}\sec \]

C) \[\frac{2\pi }{5}\sec \]   

D) none of these

Correct Answer: B

Solution :

[b] \[Mg=k\times 20-k\times 10\] \[\Rightarrow k=\frac{mg}{10/100}N/m\] \[T=2\pi \sqrt{\frac{M}{k}}\] \[=2\pi \sqrt{\frac{1}{49\times 4}}=\frac{\pi }{7}\sec \]