Physics - W.E.P. Question with Solution | TestHub

The spring constant $k$ can be calculated using the given force and compression:

$k=\frac{F}{x}=\frac{10}{0.4}=25\text{N/m}$

The elastic potential energy stored in the spring when it is compressed by $0.4\text{m}$ is:

$U=\frac{1}{2}k{x}^2=\frac{1}{2}\times 25\times (0.4{)}^2=\frac{1}{2}\times 25\times 0.16=2\text{J}$

When the spring is released, this elastic potential energy is converted into the gravitational potential energy of the sphere at its maximum height $h$ (measured from the compressed position). Using the law of conservation of energy:

$mgh=U$

Given $m=50\text{g}=0.05\text{kg}$ and $g=10{\text{m/s}}^2$, substituting the values we get:

$0.05\times 10\times h=2$

$0.5h=2$

$h=4\text{m}$

Answer: $4m$