Question

A person of mass 80 kg sits on a spring and compresses it by 2 m. If the person is projected at 20 m/s velocity by the spring, then the spring constant is (Take no energy loss):

• A. 2000
• B. 4000
• C. 6000
• D. 8000

Hint:

Always use energy conservation when spring compression is directly related to velocity.

Answer 1

The Correct Option is D

Step 1: Energy transformation.
Elastic potential energy converts entirely to kinetic energy: ½ k x² = ½ m v².

Step 2: Given data.
m = 80 kg, x = 2 m, v = 20 m/s.

Step 3: Substituting values.
½ k (2)² = ½ (80)(20)² → 2k = ½×80×400 = 16000.

Step 4: Solving for k.
k = 16000/2 = 8000 N/m.

Step 5: Conclusion.
The spring constant is 8000 N/m.