A weight of $200\,\,kg$ is suspended by vertical wire of length $600.5\,\,cm$. The area of cross-section of wire is $1\,\,m{m^2}$. When the load is removed, the wire contracts by $0.5\,\,cm$. The Young’s modulus of the material of wire will be

A steel wire of length 2 m has an elastic limit of $8 imes 10^8 \, N m^{-2}$ and a Young's modulus of $2 imes 10^{11} \, N m^{-2}$. What is the maximum elongation of the wire?

A wire of length $L$ and radius a rigidly fixed at one end. On stretching the other end of the wire with a force $F$, the increase in its length is $l$. If another wire of same material but of length 2L and radius $2a$ is stretched with a force $2F$, the increase in its length will be

When a weight $w$ is hung from one end of the wire other end being fixed, the elongation produced in it be $l$. If this wire goes over a pulley and two weights $w$ each are hung at the two ends, the elongation of the wire will be

Which of the following properties is most crucial for determining the stretching of a spring?

A force $F$ is required to break a wire of length $I$ and radius $r$. What force is required to break a wire, of the same material, having twice the length and six times the radius ?

A wire of length L and cross-sectional area A is stretched by a force F. If Young's modulus of the material of the wire is Y, the elongation produced in the wire is:

Two springs, one made of steel and the other of copper, are designed to have the same stiffness. If the steel spring has a cross-sectional area 'A', what should be the cross-sectional area of the copper spring, given that the shear modulus of steel is twice that of copper?

The elastic limit of brass is $379MPa$. What should be the minimum diameter of a brass rod, if it is to support a $400N$ load without exceeding its elastic limit

The following data were obtained when a wire was stretched within the elastic region Force applied to wire $100{\rm{ }}N$Area of cross-section of wire ${10^{ - 6}}{{\rm{m}}^2}$Extensional of wire $2 imes {10^{ - 9}}{\rm{m}}$Which of the following deductions can be correctly made from this data?I. The value of Young’s Modulus is ${10^{11}}\,{\rm{N}}{{\rm{m}}^{ - 2}}$II. The strain is ${10^{ - 3}}$III. The energy stored in the wire when the load is applied is $10{\rm{ }}J$

How much force is required to produce an increase of ${\rm{0}}{\rm{.2}}\,\,{\rm{\% }}$ in the length of a brass wire of diameter $0.6\,\,mm$ (Young’s modulus for brass $= 0.9\,\, imes {10^{11}}N/{m^2}$