To determine Young's modulus of a wire, the formula is $Y = \frac{F}{A}.\frac{L}{{\Delta L}}$ where $F/A$ is the stress and $L/\Delta L$ is the strain. The conversion factor to change $Y$ from $CGS$ to $MKS$ system is

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

In the Young’s experiment, If length of wire and radius both are doubled then the value of $Y$ will become

A wire of length $L$ and radius $r$ is clamped at one end. If its other end is pulled by a force $F$, its length increases by $l$. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become.

A $14.5\; kg$ mass, fastened to the end of a steel wire of unstretched length $1.0 \;m ,$ is whirled in a vertical circle with an angular velocity of $2\;rev/s$ at the bottom of the circle. The cross-sectional area of the wire is $0.065 \;cm ^{2} .$ Calculate the elongation of the wire when the mass is at the lowest point of its path.

Column$-II$ is related to Column$-I$. Join them appropriately :