Mechanical Properties of Solids Questions and Answers Part-10

1. On applying a stress of \[20 \times 10^{8}N\diagup m^{2}\]   the length of a perfectly elastic wire is doubled. Its Young’s modulus will be
a) \[40 \times 10^{8}N\diagup m^{2}\]
b) \[20 \times 10^{8}N\diagup m^{2}\]
c) \[10 \times 10^{8}N\diagup m^{2}\]
d) \[5 \times 10^{8}N\diagup m^{2}\]

Answer: b

2. When a uniform wire of radius r is stretched by a 2kg weight, the increase in its length is 2.00 mm. If the radius of the wire is r/2 and other conditions remain the same, the increase in its length is
a) 2.00 mm
b) 4.00 mm
c) 6.00mm
d) 8.00 mm

Answer: d

3. The length of an elastic string is 'a' metre when the longitudinal tension is 4 N and 'b' metre when the longitudinal tension is 5 N. The length of the string in metre when the longitudinal tension is 9 N is
a) \[a-b\]
b) \[5b-4a\]
c) \[2b-\frac{1}{4}a\]
d) \[4a-3b\]

Answer: b
Explanation: Let L is the original length of the wire and K is force constant of wire.

4. Stress to strain ratio is equivalent to
a) Modulus of elasticity
b) Poission’s Ratio
c) Reyhold number
d) Fund number

Answer: a
Explanation: Modulus of elasticity

5. Which is correct relation
a) \[Y<\sigma\]
b) \[Y>\sigma\]
c) \[Y=\sigma\]
d) \[\sigma=+1\]

Answer: b
Explanation: \[Y>\sigma\]

6.If the interatomic spacing in a steel wire is 3.0 Å and \[Y_{steel}=20 \times 10^{10}N\diagup m^{2}\]     then force constant is
a) \[6 \times 10^{-2}N\diagup \dot{A}\]
b) \[6 \times 10^{-9}N\diagup \dot{A}\]
c) \[4 \times 10^{-5}N\diagup \dot{A}\]
d) \[6 \times 10^{-5}N\diagup \dot{A}\]

Answer: b

7. A copper wire of length 4.0m and area of crosssection \[ 1.2cm^{2}\] is stretched with a force of \[4.8 \times 10^{3}N\]   . If Young’s modulus for copper is \[1.2 \times 10^{11}N\diagup m^{2}\]    the increase in the length of the wire will be
a) 1.33 mm
b) 1.33 cm
c) 2.66 mm
d) 2.66 cm

Answer: a

8. A metal bar of length L and area of cross-section A is clamped between two rigid supports. For the material of the rod, its Young’s modulus is Y and coefficient of linear expansion is \[\alpha\] . If the temperature of the rod is increased by \[\triangle t^{0}C\]   the force exerted by the rod on the supports is
a) \[YAL\triangle t\]
b) \[YA\alpha\triangle t\]
c) \[\frac{YL\alpha\triangle t}{A}\]
d) \[Y\alpha AL\triangle t\]

Answer: b
Explanation: \[YA\alpha\triangle t\]

9. According to Hook’s law of elasticity, if stress is increased, the ratio of stress to strain
a) Increases
b) Decreases
c) Becomes zero
d) Remains constant

Answer: d

10. A pan with set of weights is attached with a light spring. When disturbed, the mass-spring system oscillates with a time period of 0.6 s. When some additional weights are added then time period is 0.7s. The extension caused by the additional weights is approximately given by
a) 1.38 cm
b) 3.5 cm
c) 1.75 cm
d) 2.45 cm

Answer: b