Mechanical Properties of Solids

When a force F is applied on a wire oflength L and radius r, extension produce is l. If same force F is applied on the same material wire of length 2 L and radius 2r, then extension will be

• l

• 2l

• l/2

• 4l

Energy stored in the unit volume of a wire due to its elasticity is 

• $\frac{1}{2} (\mathrm{force} \times \mathrm{strain})$

• $\frac{1}{2} \mathrm{stress} \times \mathrm{strain}$

• stress/strain

• force/strain

Which of the following has maximum property of elasticity?

• Rubber

• Lead

• Wood

• Steel

Copper has face centred cubic (fcc) lattice with interatomic spacing equals to 2.54 $\stackrel{\circ }{\mathrm{A}}$. The value of lattice constant for this lattice is

• 3.59 $\stackrel{\circ }{\mathrm{A}}$

• 2.54 $\stackrel{\circ }{\mathrm{A}}$

• 1.27 $\stackrel{\circ }{\mathrm{A}}$

• 5.08 $\stackrel{\circ }{\mathrm{A}}$

A copper wire and a steel wire of the same diameter and length are connected end to end and a force is applied which stretches their combined length by 1 cm. Then the two wires will have

• the same stress and strain

• the same stress but different strain

• the same strain but different stress

• different stress and strain

A solid sphere of radius r made of a material of bulk modulus K is surrounded by a liquid in cyliridrical container. The massless piston of area A floats on the surface of the liquid. If a mass m is placed on a piston to compress the liquid, then the fractional change in the radius of the sphere will be

• $\frac{\mathrm{mg}}{\mathrm{AK}}$

• $\frac{2\mathrm{mg}}{\mathrm{AK}}$

• $\frac{3\mathrm{mg}}{\mathrm{AK}}$

• $\frac{\mathrm{mg}}{3\mathrm{AK}}$

Two wires of same material and length are stretched by the same force. Their masses are in the ratio 4 : 3. The ratio of their elongation will be

• 16 : 9

• 9 : 16

• 4 : 3

• 3 : 4

A wire suspended vertically from one of its ends is stretched by attaching a weight 100 N to the lower end. The wire stretches by 1mm. The elastic energy stored in the wire is

• 0.02 J

• 0.05 J

• 0.1 J

• 0.2 J

A circular metal plate of radius 5 cm rests on a layer of centre oil 2mm thick whose coefficient of viscosity is 15.5 dyne cm^-2 s. The value of shearing stress when a horizontal force move the plate with a speed of 5 cm/s will be

• 387.5 dyne cm^-2

• 328 dyne cm^-2

• 250 dyne cm^-2

• 428 dyne cm^-2

A steel wire of length 15 m has density = 7.7 × 10³ kg/m³ and Young's modulus = 2.2 × 10¹¹ N/m². It is subjected to a tension which produces an elastic strain of 1%. Its fundamental frequency of vibration must be

• 256 Hz

• 178 Hz

• 170 Hz

• 200 Hz