Mechanical Prop...

The force required to stretch a steel wire of $$1 cm^{2}$$ cross-section to $$1.1$$ times its length would be ($$Y =2 \times 10^{11} Nm^{-2}$$

Which statement is true for a metal

The length of a rod is $$20 cm$$ and area of cross-section $$2 cm^2$$. The Young's modulus of the material of wire is $$1.4 \times 10^{11} N/m^2$$ . If the rod is compressed by $$5 kg-wt$$ along its length, then increase in the energy of the rod in joules will be

In solids, inter-atomic forces are

If a spring is extended to length $$l$$ then according to Hook's law

A spring of force constant $$k = 100 N/m$$ is compressed to $$x = 0.5 m$$ by a block of mass $$100 g$$ and released. There should be a box placed at a distance $$d$$ on the ground so that the block falls in it. Find the distance $$d.$$ 

The equation of a stationary wave in a metal rod is given by $$y=0.002\displaystyle \sin\frac{\pi x}{3}\sin 1000t$$, where $$\mathrm{x}$$ is in cm and $$\mathrm{t}$$ is in second. The maximum tensile stress at a point $$\mathrm{x}=2\mathrm{c}\mathrm{m}$$ (Young's modulus $$\mathrm{Y}$$ of material of rod $$=8\times 10^{11}dyne/cm^{2})$$ will be

A copper wire is held at the two ends between two rigid supports. At $$30^{\mathrm{o}}\mathrm{C}$$, the wire is just taut,with negligible tension. If $$Y=13\times 10^{11}Nm^{-2}, \alpha =1.7\times 10^{-5}(^{\circ}C)^{-1}$$ and density $$ \rho=9\times 10^{3}kgm^{-3}$$, then the speed of transverse wave in this wire at $$10^{o}$$C is:

 In performing an experiment to determine the Young's modulus Y of steel, a  student can record the following values:
length of wire l$$=(\ell_{0}\pm\Delta$$l$$){m}$$
diameter of wire $${d}=({d}_{0}\pm\Delta {d})$$ mm
force applied to wire $${F}$$=$$({F}_{0}\pm\Delta {F}){N}$$
extension of wire $${e}=({e}_{0}\neq\Delta {e})$$ mm
In order to obtain more reliable value for Y, the followlng three techniques are suggested.
Technique (i) A shorter wire ls to be used.
Technique (ii) The diameter shall be measured at several places with a micrometer screw gauge.
Technique (iii) Two wires are made irom the same ntaterial and of same length. One is loaded at a fixed weight and acts as a reference for the extension of the other which is load- tested
Which of the above techniques is/are useful?

In the figure above, a wire is subjected to a gradually increasing  force  $${F}_{i}$$ which causes an extension e. The way in which e depends on F is shown by the line OP. Then, the force is gradually decreased and relation between e and F in this case is shown by the line PQ. The mechanical energy that is recovered from the wire in this process when the force is removed, is given by the shaded area in