The dimensional formula for Young's modulus is

$A$ force of $200\, N$ is applied at one end of a wire of length $2\, m$ and having area of cross-section $10^{-2}\, cm^2$. The other end of the wire is rigidly fixed. If the coefficient of linear expansion of the wire is $\alpha = 8 \times 10^{-6}\, ^\circ C^{-1}$,Young's modulus is $Y = 2.2 \times 10^{11}\, N/m^2$,and its temperature is increased by $5\, ^\circ C$,then the increase in the tension of the wire will be ........ $N$.

$A$ force of $10^3 \ N$ stretches the length of a hanging wire by $1 \ mm$. The force required to stretch a wire of the same material and length,but having four times the diameter,by $1 \ mm$ is:

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

$A$ wire of cross-section $4 \; mm^2$ is stretched by $0.1 \; mm$ by a certain weight. How far (length) will a wire of the same material and length but of area $8 \; mm^2$ stretch under the action of the same force?

An object of mass $m$ is suspended at the end of a massless wire of length $L$ and area of cross-section $A$. The Young's modulus of the material of the wire is $Y$. If the mass is pulled down slightly,its frequency of oscillation along the vertical direction is: