Question

A block of mass \(m\) is moving on a horizontal frictionless surface with velocity \(v\). It hits a spring of constant \(k\) and compresses it by a distance \(x\). If the initial velocity is doubled, what will be the new compression?

• A. \(2x\)
• B. \(\sqrt{2}\,x\)
• C. \(4x\)
• D. \(x/2\)
• E.

Hint:

In spring–block energy problems, equate kinetic energy with spring potential energy. Since \(x^2 \propto v^2\), the compression \(x\) is directly proportional to the velocity \(v\). If velocity doubles, compression doubles; if velocity quadruples, compression quadruples.

Answer 1

The Correct Option is A