Question

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

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

Answer 1

The correct option is A $0.15m$

At maximum compression K.E of block will be zero.

By energy conservation, $\frac{1}{2}m{v}^2=\frac{1}{2}k{x}^2$

$\frac{1}{2}\times 0.5\times (1.5{)}^2=\frac{1}{2}\times 50(x{)}^2$

$x^2=\frac{(1.5{)}^2}{100}=(\frac{1.5}{10}{)}^2$

$x=0.15m$