The mass and length of a wire are $M$ and $L$ respectively. The density of the material of the wire is $d$. On applying the force $F$ on the wire, the increase in length is $l$, then the Young's modulus of the material of the wire will be

In suspended type moving coil galvanometer, quartz suspension is used because

$A$ rod of length $1000\, mm$ and coefficient of linear expansion $a = 10^{-4}$ per degree is placed symmetrically between fixed walls separated by $1001\, mm$. The Young’s modulus of the rod is $10^{11} N/m^2$. If the temperature is increased by $20^o C$, then the stress developed in the rod is ........... $MPa$

A wire is stretched by $0.01$ $m$ by a certain force $F.$ Another wire of same material whose diameter and length are double to the original wire is stretched by the same force. Then its elongation will be

Explain with illustration cranes regarding the applications of elastic behaviour of materials.

The length of an elastic string is a metre when the longitudinal tension is $4\, N$ and $b$ metre when the longitudinal tension is $5\, N$. The length of the string in metre when the longitudinal tension is $9\, N$ is