Poisson's Effect

Q. The famous Big Ben clock tower in London has hour hand of approximate length $10$ feet. Calculate the magnitude of change in velocity of the tip of the hour hand of Big Ben in $6$ hours $(1feet=0.305m)$

1. $0.4189m/s$
2. $0.341m/s$
3. $0.06912m/s$
4. $0.887mm/s$

Q. There is no change in the volume of a wire due to change in its length on stretching. The poisson's ratio of the material of the wire is

1. $-\frac{1}{2}$
2. $\frac{1}{2}$
3. $-\frac{1}{4}$
4. $\frac{1}{4}$

Q. The Poisson’s ratio of the 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 its length is

1. 2.5%
2. 4%
3. 1%
4. 2%

Q.

Two wires of diameter 0.25 cm, one made of steel and the other made of brass are loaded as shown in Fig. 9.13. The unloaded length of steel wire is 1.5 m and that of brass wire is 1.0 m. Compute the elongation of the steel and the brass wires.

Q.

What is the dimensional formula for compressibility?

Q. A material has Poisson's ratio $0.5$. If a uniform rod made of it suffers a longitudinal strain $2\times {10}^{-3}$. What is the percentage increase in volume?

Q. The lateral strain produced in the wire is $0.01\times {10}^{-3}$. If Poisson's ratio is $0.4$, then find the longitudinal strain produced in the wire.

1. $5\times {10}^{-5}$
2. $1.25\times {10}^{-5}$
3. $10\times {10}^{-5}$
4. $2.5\times {10}^{-5}$

Q. The shear modulus of a liquid is:

1. Zero
2. Unity
3. Infinity
4. None

Q. A metal wire is stretched by a load. Then the fractional change in its volume $\frac{\Delta V}{V}$ is proportional to

1. $\sqrt{\frac{\Delta L}{L}}$
2. $\frac{\Delta L}{L}$
3. ${\left(\frac{\Delta L}{L}\right)}^3$
4. ${\left(\frac{\Delta L}{2}\right)}^2$

Q. Poisson's ratio is the ratio of lateral strain to the longitudinal strain.

1. True
2. False

Q. A compressive force is applied to a uniform rod of rectangular cross-section so that its length decreases by 1%. If the Poisson's ratio for the material of the rod be $0.2$, then volume approximately decreases by (in percentage).

Q. ABC is an equilateral triangle of side 1. M. D is the midpoint of BC. Charges of 4C, 4C and 3C are placed at B, C and D respectively. Find the resultant electric intensity at A.

1. $2\times {10}^{9}N{C}^{-1}$
2. $24\times {10}^{9}N{C}^{-1}$
3. $48\times {10}^{9}N{C}^{-1}$
4. $36\times {10}^{9}N{C}^{-1}$

Q.

A steel wire is stretched by a certain amount under a load. if the load and the radius both are increasing to 4 times find the stretch cause in wire

Q. Find the value of poission's ratio $\left(\mu \right)$ of a material whose bulk modulus$\left(K\right)$ value is half of its young's modulus $\left(Y\right)$ value.

1. $\frac{1}{3}$
2. $\frac{1}{6}$
3. $\frac{1}{4}$
4. $\frac{1}{2}$

Q. a mild steel wire of length 1 m and cross-sectional area 0.005 cm2 is stretched, well within its elastic limit, horizontally b/w two pillars. a mass of 100 g is suspended form the mid point of the wire. calculate the depression at mid point.

Q. A steel rod of $10\text{mm}$ diameter is loaded with a force of $20\text{kN}$. Change in diameter of the rod is $3.82\times {10}^{-3}\text{mm}$ . Given, Young's modulus for steel is $200\text{GPa}$, find its Poisson's ratio.

1. $0.30$
2. $0.28$
3. $0.21$
4. $0.88$

Q. Four wires of the same material are stretched by the same load . The dimensions are given below . Which of them will elongate the most ? and why ???

LENGTH DIAMETER
a) 100cm 1mm
b) 200cm 2mm
c) 300cm 3mm
d) 400cm 0.5mm

Q.

When a load of 20 kg is hung from a wire is cross-sectional area 1 sq mm, it's elongated length is 600.5 cm. If the load is withdrawn the wire shrinks by 0.5 cm in length. Calculate the youngs modulus of the wire?

Q.

A load of 10 kg is suspended by a metal wire 3 m long and hvaing a cross- sectional area $4m{m}^2$. Find (a) the stress (b) the strain and (c) the elongation. Young modulus of the metal is 2.0 $\times {10}^{11}N{m}^{-2}$.

Q. What is the relation between Modulus of rigidity$\left(G\right),$ Youngs modulus $\left(Y\right)$ and Bulk modulus$\left(B\right)$ ?

1. $\frac{1}{Y}=\frac{1}{B}+\frac{1}{G}$
2. $\frac{3}{Y}=\frac{1}{3B}+\frac{1}{G}$
3. $\frac{1}{Y}=\frac{3}{B}+\frac{1}{G}$
4. $\frac{1}{3Y}=\frac{1}{B}+\frac{3}{G}$

Q.

Two rods of identical dimension with youngs modulli Y1 and Y2 are joined end to end . The equivalent youngs modulus for the composite rod is (if the equivalent rod is also having same dimension as of the original rods)

Q.

Two wires one of Steel and other of aluminium each of 2 m long and diameter 20 mm are joined end to end and a composite wire of 4 m is formed. What is the tension in the wire producef on a total extension of 0.9 millimetres?

Q. A steel wire of cross sectional area $0.05{\text{cm}}^2$ is under a tension of $15\text{N}$. Find the decrease in the cross-sectional area. Young's modulus of steel = $2\times {10}^{11}{\text{N/m}}^2$ and Poisson's ratio = $0.3$.

1. $40\times {10}^{-8}{\text{cm}}^2$
2. $50\times {10}^{-8}{\text{cm}}^2$
3. $45\times {10}^{-8}{\text{cm}}^2$
4. $22.5\times {10}^{-8}{\text{cm}}^2$

Q. There is no change in the volume of a wire due to change in its length on stretching. The Poisson’s ratio of the material of the wire is

1. 
2. 
3. 
4. 

Q. A stone is rotated steadily in a horizontal circle with a time period $T$ by means of a string of length $\ell$. If the tension in the string is kept constant and length $\ell$ increase by $1\%$ then percentage change in time period $T$ is

1. $1\%$
2. $2\%$
3. $0.5\%$
4. $0.25\%$

Q.

In Hookes law, the constant of proportionality signifies?

Q. Which is correct relation. ($\sigma$ is Poisson's Ratio, Y is the young's Modulus)

1. Y > σ
2. σ = +1
3. Y = σ
4. Y < σ

Q. For a given material, the Youngs modulas is $2.4$ times its modulus of rigidity. What is the value of its poissons ratio ?

1. $0.5$
2. $0.4$
3. $0.2$
4. $0.3$

Q. Two persons A and B of weight 60 kg and 40 kg respectively stand facing each other, and pullon a light rope stretched between them. Find the ratio of their distance covered by them when they meet if their initial Separation was 5 m.

Q. Find the value of poission's ratio $\left(\mu \right)$ of a material whose bulk modulus$\left(K\right)$ value is half of its young's modulus $\left(Y\right)$ value.

1. $\frac{1}{3}$
2. $\frac{1}{6}$
3. $\frac{1}{4}$
4. $\frac{1}{2}$