Question

A car of mass $1000kg$ moving with a speed $18km{h}^{-1}$ on a smooth road and colliding with a horizontally mounted spring of spring constnat $6.25\times {10}^{3}N{m}^{-1}$. The maximum compression of the spring is

• A. $1m$
• B. $2m$
• C. $3m$
• D. $4m$

Answer 1

The correct option is B $2m$

Here,
$m=1000kg,v=18km{h}^{-1}=18\times \frac{5}{18}m{s}^{-1}=5m{s}^{-1}$
$k=6.25\times {10}^{3}N{m}^{-1}$
At maximum compression $x_m$, the kinetic energy of the car is converted entirely into the potential energy of the spring.
$\therefore \frac{1}{2}m{v}^2=\frac{1}{2}k{x}_m^2$ or $x_m=\sqrt{\frac{m}{k}}v$
Substituting the given values, we get
$x_m=\sqrt{\frac{1000kg}{6.25\times {10}^{2}N{m}^{-1}}}\times 5m{s}^{-1}=0.4\times 5m=2m$.