The length of a spring is a when $\alpha $ force of $4\,N$ is applied on it and the length is $\beta $ when $5\,N$ force is applied. Then the length of spring when $9\,N$ force is applied is

Give the example of variable force. Write the formula of Hook’s law.

A ball is dropped from a height of $80\,m$ on a surface which is at rest. Find the height attainded by ball after $2^{nd}$ collision if coefficient of restitution $e = 0.5$ ............ $\mathrm{m}$

The work done in joules in increasing the extension of a spring of stiffness $10\, N/cm$ from $4\, cm$ to $6\, cm$ is:

An engine is attached to a wagon through a shock absorber of length $1.5\,m$. The system with a total mass of $50,000 \,kg$ is moving with a speed of $36\, km\,h^{-1}$ when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by $1.0\,m$.

If $90\%$ of energy of the wagon is lost due to friction, calculate the spring constant.

In stretching a spring by $2\,cm$ energy stored is given by $U,$ then more stretching by $10\,cm$ energy stored will be