Two wires $A$ and $B$ are of same materials. Their lengths are in the ratio $1 : 2$ and diameters are in the ratio $2 : 1$ when stretched by force ${F_A}$ and ${F_B}$ respectively they get equal increase in their lengths. Then the ratio ${F_A}/{F_B}$ should be

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

The Young's modulus of a wire of length $L$ and radius $r$ is $Y$ $N/m^2$. If the length and radius are reduced to $L/2$ and $r/2,$ then its Young's modulus will be

A uniform wire (Young's modulus $2 \times 10^{11}\, Nm^{-2}$ ) is subjected to longitudinal tensile stress of $5 \times 10^7\,Nm^{-2}$ . If the over all volume change in the wire is $0.02\%,$ the fractional decrease in the radius of the wire is close to

check the statment are True or False $:$

$(a)$ Young’s modulus of rigid body is .....

$(b)$ A wire increases by $10^{-6}$​ times its original length when a stress of
$10^8\,Nm^{-2}$ is applied to it, calculate its Young’s modulus.

$(c)$ The value of Poisson’s ratio for steel is ......