One end of a massless spring of spring constant 100 N/m and natural length 0.5 m is fixed and the other end is connected to a particle of mass 0.5 kg lying on as frictionless horizontal table. The spring remains horizontal. If the mass is made to rotate at an angular velocity of 2 rad/s, find the elongation of the spring.

Explanation

To solve the problem, we need to find the elongation of the spring when a mass is rotating at a certain angular velocity. Here’s the step-by-step solution:

### Step 1: Understand the system
We have a mass \( m = 0.5 \, \text{kg} \) attached to a spring with a spring constant \( k = 100 \, \text{N/m} \). The natural length of the spring is \( L_0 = 0.5 \, \text{m} \). The mass is rotating with an angular velocity \( \omega = 2 \, \text{rad/s} \).

### Step 2: Set up the equations
When the mass rotates, the spring stretches by an elongation \( x \). The total length of the spring when stretched is:
\[
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