### JEE Main On 8 April 2017 Question 5

##### Question: 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]

#### Options:

A) 2 Hz

B) $ \frac{1}{4}Hz $

C) $ \frac{1}{2\sqrt{2}}Hz $

D) $ \frac{1}{2}Hz $

## Show Answer

#### Answer:

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 $