$A$ block of mass $m$ moving at a speed $v$ compresses a spring through a distance $x$ before its speed becomes one fourth. Find the spring constant of the spring.

When a spring is stretched by a distance $x$,its potential energy is $10 \ J$. The work done to stretch this spring by an additional distance $x$ is ........ $J$.

$A$ block of mass $m=25 \ kg$ sliding on a smooth horizontal surface with a velocity $v=3 \ ms^{-1}$ meets a spring of spring constant $k=100 \ N/m$ fixed at one end as shown in the figure. The maximum compression of the spring and the velocity of the block as it returns to the original position are, respectively:

Two springs have their force constants as $k_1$ and $k_2$ $(k_1 > k_2)$. When they are stretched by the same force $F$,which of the following statements is true regarding the work done?

In the figure,the ball $A$ is released from rest when the spring is at its natural (unstretched) length. For the block $B$ of mass $M$ to leave contact with the ground at some stage,the minimum mass of $A$ must be

When a long spring of $4 \ cm$ is stretched by $1 \ cm$,the potential energy stored in the spring is $U$. If it is stretched by $4 \ cm$,the potential energy stored in it is (in $U$)