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 $k = 50 \,N/m$. The maximum compression of the spring would be :

• A. 0.15 m
• B. 0.12 m
• C. 1.5 m
• D. 0.5 m

Answer 1

Answer: (A)

By the law of conservation of energy,
kinetic energy of mass = energy stored in spring
i.e., $ \frac{1}{2}m{{v}^{2}}=\frac{1}{2}k{{x}^{2}} $
$ \therefore $ $ {{x}^{2}}=\frac{m{{v}^{2}}}{k} $
$ \Rightarrow $ $ x=\sqrt{\left( \left. \frac{m{{v}^{2}}}{k} \right) \right.} $
$ \Rightarrow $ $ x=\sqrt{\left( \frac{0.5\times 1.5\times 1.5}{50} \right)} $
So, $ x=0.15\,m $