Mechanical Properties of Solids Test

Result

Mechanical Properties of Solids Test - 70

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Weekly Quiz Competition

Question 1
1 / -0

The graph shows the extension of a sample of a type of rubber as different loads F are applied and then gradually removed.
What is the best estimate of the strain energy in the rubber when a load of $$80$$ N is applied?

A
$$0.40$$ J

B
$$0.64$$ J

C
$$0.88$$ J

D
$$1.3$$ J
Question 2
1 / -0

In an experiment, bras and steel wires of length lm each with areas of cross section $$1 mm^2$$ are used. the wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress required to produce a net elongation of $$0.2 mm$$ is :
(Given, the Young's Modulus for steel and brass are respectively, $$120 \times 10^9 N/m^2$$ and $$60 \times 10^9 N/m^2$$)

A
$$0.2 \times 10^6 N/m^2$$

B
$$4.0 \times 10^6 N/m^2$$

C
$$1.8 \times 10^6 N/m^2$$

D
$$1.2 \times 10^6 N/m^2$$

Solution

$$k_1 = \dfrac{y_1 A_1}{\ell_1} = \dfrac{120 \times 10^9 \times A}{1}$$
$$k_2 = \dfrac{y_2 A_2}{\ell_2} = \dfrac{60 \times 10^9 \times A}{1}$$
$$k_{eq} = \dfrac{k_1 k_2}{k_1 \times k_2} = \dfrac{120 \times 60}{180} \times 10^9 \times A$$
$$k_{eq} = 40 \times 10^9 \times A$$
$$F = k_{eq} (x)$$
$$F = (40 \times 10^9) A. (0.2 \times 10^{-3})$$
$$\dfrac{F}{A} = 8 \times 10^6 N/m^2$$
No option is matching.Hence question must be bonus.
Question 3
1 / -0

The bulk modulus for an incompressible liquid is?

A
$$\infty$$

B
$$0$$

C
$$1$$

D
$$2$$

Solution

Bulk Modulus $$K= \dfrac{-dP}{ (dV/V)} =-\dfrac{VdP}{dV}$$

For incompressible fluid, $$dV = 0$$
On putting the value of $$dV$$

$$K=\dfrac{Vdp}{0}=\infty$$

Option A
Question 4
1 / -0

To determine the Young modulus of a wire, several measurements are taken.
In which row can the measurement not be taken directly with the stated apparatus?

A
measurement : area of cross-section of wire ; apparatus : micrometer screw gauge

B
measurement : extension of wire ; apparatus : vernier scale

C
measurement : mass of load applied to wire ; apparatus : electronic balance

D
measurement : original length of wire ; apparatus : metre rule

Solution

Measurement of area of any object is not a proper way of measuring .
Instead of measuring area , one should have to measure the diameter.
So, option A is correct answer.
Question 5
1 / -0

Young's modulus is defined for:

A
Solid

B
Liquid

C
Gas

D
All of these

Solution
Question 6
1 / -0

From the ceiling, a light rod of length $$200$$ cm is suspended horizontally with the help of two vetical wires of equal lenght as shown in figure. If one wire is made of brass and have cross-sectional area $$0.2$$ $$cm^2$$ and other of steel of $$0.1$$ $$cm^2$$ of cross-sectional area, then at what distance along rod a weight may be hung to produce equal stress in both the wires?

A
$$\dfrac{4}{3}$$ m from steel wire

B
$$\dfrac{4}{3}$$ m from brass wire

C
$$1$$ m from steel wire

D
$$\dfrac{1}{4}$$ m from brass wire

Solution
Question 7
1 / -0

The dimensions of Poisson's ratio is?

A
$$[M^0L^0T^0]$$

B
$$[ML^{-1}T^{-2}]$$

C
$$[ML^2T^{-4}]$$

D
$$[ML^2T^{-3}]$$

Solution
Question 8
1 / -0

The stress for one litre of a perfect gas, at a pressure of $$72$$ cm of Hg, when it is compressed isothermally to a volume of $$900$$ cc, is?

A
$$9.88\times 10^3$$ $$N/m^2$$

B
$$10.88\times 10^3$$ $$N/m^2$$

C
$$1.088\times 10^3$$ $$N/m^2$$

D
$$2\times 10^3$$ $$N/m^2$$

Solution
Question 9
1 / -0

A rod of length $$1000$$ min and coefficient of linear expansion $$\alpha =10^{-4}$$ per degree is placed symmetrically between fixed walls separated by $$1001$$ mm. The Young's modulus of the rod is $$10^{11}$$ $$N/m^2$$. If the temperature is increased by $$20^oC$$, then the stress developed in the rod is (in $$N/m^2$$):

A
$$10$$

B
$$2\times 10^8$$

C
$$10^8$$

D
Cannot be calculated

Solution
Question 10
1 / -0

If for a material, Y and B are Young's modulus and Bulk modulus then:

A
$$Y < 3B$$

B
$$Y=3B$$

C
$$Y > 3B$$

D
$$3Y=B$$

Solution