Mechanical Prop...

At $$40^oC$$, a brass wire of $$1 mm$$ radius is hung from the ceiling. A small mass, $$M$$ is hung from the free end of the wire. When the wire is cooled down from $$40^oC$$ to $$20^oC$$ it regains its original length of $$0.2 m$$. The value of $$M$$ is close to :
(Coefficient of linear expansion and Young's modulus of brass are $$10^{-5} / ^oC$$ and $$10^{11} \ N/m^2$$, respectively; $$g = 10 ms^{-2}$$)

Temperature of a gas is $$20^{0}\mathrm{C}$$ and pressure is changed from $$1.01\times 10^{5}$$ Pa to $$1.165\times 10^5\mathrm{P}\mathrm{a}$$. If volume is decreased isothermally by 10%. The bulk modulus of gas is (in $$Pa$$):

$$\mathrm{A}$$ student performs an experiment to determine the Young's modulus of a wire, exactly 2 $$\mathrm{m}$$ long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be $$0.8 mm$$ with an uncertainty of $$\pm 0.05$$ mm at a load of exactly $$1.0 kg$$. The student also measures the diameter of the wire to be $$0.4 mm$$ with an uncertainty of $$\pm 0.01$$ mm. Take $$\mathrm{g}=9.8\mathrm{m}/\mathrm{s}^{2}$$ (exact). The Young's modulus obtained from the reading is 

One end of a horizontal thick copper wire of length $$2L$$ and radius $$2R$$ is welded to an end of another horizontal thin copper wire of length $$L$$ and radius $$R$$. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is:

Dimensions of stress are :

The bulk modulus of a spherical objects is '$$B$$'. If it is subjected to uniform pressure '$$P$$', the fractional decrease in radius is:

Copper of fixed volume 'V' is drawn into wire of length 'l'. When this wire is subjected to a constant force 'F', the extension produced in the wire is $$'\Delta l'$$. Which of the following graph is a straight line?

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?

The Young's modulus of steel is twice that of brass. Two wires of sample length and of same area of cross section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of:

The length of a metal wire is $$l_1$$ when the tension in it is $$T_1$$ and is $$I_2$$ when the tension is $$T_2$$. The natural length of the wire is?