Question

A mass of 0.5 kg moving with a speed of 1.5 m/s on a horizontal smooth surface, collides with a nearly weightless spring of force constant \( k = 50 \, \text{N/m} \). The maximum compression of the spring would be:

• A. 0.5 m
• B. 0.12 m
• C. 0.15 m
• D. 15 m

Hint:

In problems involving springs, use energy conservation to relate kinetic and potential energies.

Answer 1

The Correct Option is C

Step 1: Energy conservation.
The initial kinetic energy of the mass is converted into potential energy of the spring at maximum compression. The equation is: \[ \frac{1}{2} m v^2 = \frac{1}{2} k x^2 \] Step 2: Solving for \( x \).
Substituting the given values: \[ \frac{1}{2} (0.5) (1.5)^2 = \frac{1}{2} (50) x^2 \] Solving for \( x \), we get: \[ x = 0.15 \, \text{m} \]
Final Answer: \[ \boxed{0.15 \, \text{m}} \]