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

114.

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

A wire canbe brokenbyapplyinga load of200 N. The force required to break another wire of the same length and same material, but double in diameter, is

•  200 N

• 400 N

• 600 N

• 800 N

A cube of side 40 mm has its upper face displaced by 0.1 mm by a  tangenbtial force of 8 kN. The shearing modulus of cube is

• 2 × 10⁹ Nm^-2

• 4 $$\begin{gathered} \mathrm{Shearing} \mathrm{modulus} \mathrm{of} \mathrm{cube} \\ \mathrm{\eta } = \frac{\mathrm{Fl}}{\mathrm{A}∆\mathrm{l}} = \frac{8 \times {10}^3 \times 40 \times {10}^{-3}}{{\left(40 \times {10}^{-3}\right)}^2 \times \left(0.1 \times {10}^{-3}\right)} \\ = 2 \times {10}^{9 } {\mathrm{Nm}}^{-2} \end{gathered}$$ Nm^-2

• 8 × 10⁹ Nm^-2

• 16 × 10⁹ Nm^-2

A wire of length L and area of cross-section A is stretched through a distance x metre by applying a force F along length, then the work done in this process is (Y is Young's modulus of the material)

• $\frac{1}{2} \left(\mathrm{A} . \mathrm{L}\right) \left(\frac{\mathrm{Yx}}{\mathrm{L}}\right) \left(\frac{\mathrm{x}}{\mathrm{L}}\right)$

• $\left(\mathrm{A} .\hspace{0.17em}\mathrm{L}\right) \left(\mathrm{YL}\right) \left(\frac{\mathrm{x}}{\mathrm{L}}\right)$

• $2\left(\mathrm{A} . \mathrm{L}\right) \left(\mathrm{YL}\right) \left(\frac{\mathrm{x}}{\mathrm{L}}\right)$

• $3 \left(\mathrm{A} . \mathrm{L}\right) \left(\mathrm{YL}\right) \left(\frac{\mathrm{x}}{\mathrm{L}}\right)$

The modulus of elasticity is dimensionally equivalent to

• strain

• force

• stress

• coefficient of viscosity

Which of the following substance has the highest elasticity ?

• Steel

• Copper

• Rubber

• Sponge

The Poisson's ratio of a material is 0.5. If a force is applied to a wire of this material, there is a decrease in the cross-sectional area by 4%. The percentage increase in the length is

• 1 %

• 2 %

• 2.5 %

• 4 %