question_answer

A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an 8 kg block placed on the same table. So, the frequency of vibration of the 8 kg block is - [JEE Online 08-04-2017]

A)  2 Hz                                      

B) \[\frac{1}{4}Hz\]

C) \[\frac{1}{2\sqrt{2}}Hz\]                              

D) \[\frac{1}{2}Hz\]

Correct Answer: D

Solution :

 \[F=\frac{1}{2\pi }\sqrt{\frac{k}{m}}=1\]\[4{{\pi }^{2}}=\frac{k}{m}m=1\]                 \[k=4{{\pi }^{2}}\]In parallel \[{{k}_{eq}}=2k\] \[F=\frac{1}{2\pi }\sqrt{\frac{K\times 2}{8}}\]     \[=\frac{1}{2}Hz\]