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

$A$ spring with spring constant $k$ is extended from $x = 0$ to $x = x_1$. The work done will be

$A$ 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.

$A$ sphere of mass $25 \,g$ is placed on a vertical spring. The spring is compressed by $0.2 \,m$ using a force of $5 \,N$. When the spring is released, the mass reaches a maximum height of (take $g = 10 \,m/s^2$):

One end of a spring of spring constant $80 \ Nm^{-1}$ and unstretched length of $30 \ cm$ is fixed at point $A$ and the other end of the spring is fitted with a smooth ring of mass $300 \ g$ as shown in the figure. The ring is allowed to slide on a horizontal rod fixed at a height of $40 \ cm$. Initially the spring makes an angle of $60^{\circ}$ with the vertical and the system of spring and ring is released from rest. The speed of the ring when the spring becomes vertical is . . . . . . $ms^{-1}$.

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 the energy of the wagon is lost due to friction,calculate the spring constant.