Two wires of the same material have lengths in the ratio 1 : 2 and their radii are in the ratio $1:\sqrt 2 $. If they are stretched by applying equal forces, the increase in their lengths will be in the ratio

A wire of area of cross-section ${10^{ - 6}}{m^2}$ is increased in length by $0.1\%$. The tension produced is $1000 N$. The Young's modulus of wire is

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 exactly similar wires of steel and copper are stretched by equal forces. If the total elongation is $2 \,cm$, then how much is the elongation in steel and copper wire respectively? Given, $Y_{\text {steel }}=20 \times 10^{11} \,dyne / cm ^2$, $Y_{\text {copper }}=12 \times 10^{11} \,dyne / cm ^2$

Two wires $A$ and $B$ of same length, same area of cross-section having the same Young's modulus are heated to the same range of temperature. If the coefficient of linear expansion of $A$ is $3/2$ times of that of wire $B$. The ratio of the forces produced in two wires will be

On applying a stress of $20 \times {10^8}N/{m^2}$ the length of a perfectly elastic wire is doubled. Its Young’s modulus will be