A spring of force constant $k$ is cut in two parts at its one third length. When both the parts are stretched by same amount, the work done in the two parts, will be

A massless platform is kept on a light elastic spring as shown in fig. When a sand particle of mass $0.1\; kg$ is dropped on the pan from a height of $0.24 \;m$, the particle strikes the pan and spring is compressed by $0.01\; m$.

From what height should the particle be dropped to cause a compression of $0.04\; m$.

$A$ block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal surface strikes and compresses a spring of stiffness $k$ till 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 According to the observer $A$

A block of mass $m$, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant $k$. The other end of the spring is fixed, as shown in the figure. The block is initially at rest in a equilibrium position. If now the block is pulled with a constant force $F$, the maximum speed of the block is

$A$ spring block system is placed on a rough horizontal floor. The block is pulled towards right to give spring an elongation less than $\frac{{2\mu mg}}{K}$ but more than $\frac{{\mu mg}}{K}$ and released.The correct statement is

When a $1.0\,kg$ mass hangs attached to a spring of length $50 cm$, the spring stretches by $2 \,cm$. The mass is pulled down until the length of the spring becomes $60\, cm.$ What is the amount of elastic energy stored in the spring in this condition, if $g = 10 m/s^{2}$ ............. $\mathrm{Joule}$