Physics · JEE | WORK, ENERGY AND POWER

When a car of mass \( m \) moving with initial speed \( v \) collides with a horizontally mounted spring of spring constant \( k \) on a rough surface with coefficient of kinetic friction \( \mu \), the quadratic equation determining the maximum compression \( x_m \) is:

1. A
   \( \frac{1}{2}kx_m^2 + \frac{1}{2}\mu mg x_m - \frac{1}{2}mv^2 = 0 \)
2. B
   \( \frac{1}{2}kx_m^2 - \mu mg x_m + \frac{1}{2}mv^2 = 0 \)
3. C
   \( kx_m^2 + \mu mg x_m - mv^2 = 0 \)
4. D
   \( \frac{1}{2}kx_m^2 + \mu mg x_m - \frac{1}{2}mv^2 = 0 \)