A stone is tied to an elastic string of negligible mass and spring constant $k$. The unstretched length of the string is $L$ and has negligible mass. The other end of the string is fixed to a nail at a point $P$. Initially the stone is at the same level as the point $P$. The stone is dropped vertically from point $P$.

$(a)$ Find the distance $'y'$ from the top when the mass comes to rest for an instant, for the first time.

$(b)$ What is the maximum velocity attained by the stone in this drop ?

$(c)$ What shall be the nature of the motion after the stone has reached its lowest point ?

The length of a wire is $1.0\, m$ and the area of cross-section is $1.0 \times {10^{ – 2}}\,c{m^2}$. If the work done for increase in length by $0.2\, cm$ is $0.4\, joule$, then Young's modulus of the material of the wire is

Two wires of diameter $0.25 \;cm ,$ one made of steel and the other made of brass are loaded as shown in Figure. The unloaded length of steel wire is $1.5 \;m$ and that of brass wire is $1.0 \;m .$ Compute the elongations of the steel and the brass wires.

A thick rope of density $\rho$ and length $L$ is hung from a rigid support. The Young's modulus of the material of rope is $Y$. The increase in length of the rope due to its own weight is

The force constant of a wire does not depend on