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)

0.15 m

Answer 2

The kinetic energy of mass is converted into energy required to compress a spring which is given by
$\Rightarrow \, \, \, \frac{1}{2}mv^2=\frac{1}{2}kx^2$
$\Rightarrow \, \, x=\sqrt{\frac{mv^2}{k}}$
$=\sqrt{\frac{0.5 \times (1.5)^2}{50}}=0.15\,m$.