$A$ 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 $g = 10 \,m/s^2$):

$A$ sphere of mass $m$ is attached to a spring of spring constant $k$ and is held in an unstretched position over an inclined plane as shown in the figure. After letting the sphere go,find the maximum length by which the spring extends,given the sphere only rolls.

Explain the elastic potential energy of a spring and obtain an expression for this energy.

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?

The spring is initially in an unstretched condition. It is first stretched by a length $x$ and the work done is $W_1$. Then again it is stretched by a further length $x$ such that the total extension becomes $2x$. The work done in this second step is $W_2$. The value of $W_2$ is given by

$A$ 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: