1.

A car of mass 1000 kg moving with a speed `18 km h^(-1)` on a smooth road and colliding with a horizontally mounted spring of spring constant `6.25 xx10^3 N m^(-1)`. The maximum compression of the spring isA. 1 mB. 2 mC. 3 mD. 4 m

Answer» Correct Answer - B
Here,
m=1000 kg , v=18 km `h^(-1) = 18xx 5/18 m s^(-1) =5 m s^(-1)`
`k=6.25 xx 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 1/2mv^2=1/2kx_m^2 " " or " " x_m=sqrt(m/k)v`
Substituting the given values , we get
`x_m=sqrt((1000 kg)/(6.25xx10^3 N m^(-1)))xx 5m s ^(-1) =0.4xx5 m=2 m`


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