If a long spring is stretched by $0.02\, m$,its potential energy is $U$. If the spring is stretched by $0.1\, m$,then its potential energy will be

$A$ bungee jumper is jumping with the help of an elastic ideal rope (force constant $K$). The jumper steps off the bridge and falls from rest towards the river below. He does not hit the water. The mass of the jumper is $m$,and the natural length of the rope is $l$. Gravity is $g$. Assuming everything is ideal,choose the incorrect option.

When a spring is stretched by $2 \, cm$,it stores $100 \, J$ of energy. If it is stretched further by $2 \, cm$,the stored energy will be increased by ............. $J$.

The force constants of two springs are $K_1$ and $K_2$. Both are stretched until their elastic potential energies are equal. If the stretching forces applied are $F_1$ and $F_2$,then the ratio $F_1:F_2$ is:

$A$ spring has a spring constant $200 \,N/m$. If it is stretched by $1 \,cm$, then the potential energy stored in it is: (in $\,J$)

$A$ block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal surface strikes and compresses a spring of stiffness $k$ until the mass comes to rest,as shown in the figure. This phenomenon is observed by two observers:
$A$: standing on the horizontal surface
$B$: standing on the block
To an observer $A$,the work done by the spring force is