Mechanical Properties of Solids Questions and Answers Part-11

1. A uniform plank of Young’s modulus Y is moved over a smooth horizontal surface by a constant horizontal force F. The area of cross section of the plank is A. The compressive strain on the plank in the direction of the force is
a) \[F\diagup AY\]
b) \[2F\diagup AY\]
c) \[\frac{1}{2}\left(F\diagup AY\right)\]
d) \[3F\diagup AY\]

Answer: a

2.The mean distance between the atoms of iron is \[3\times 10^{-10}m\]   and interatomic force constant for iron is 7 N/m The Young’s modulus of elasticity for iron is
a) \[2.33\times 10^{5}N\diagup m^{2}\]
b) \[23.3\times 10^{10}N\diagup m^{2}\]
c) \[233\times 10^{10}N\diagup m^{2}\]
d) \[2.33\times 10^{10}N\diagup m^{2}\]

Answer: d

3. Two wires A and B are of same materials. Their lengths are in the ratio 1 : 2 and diameters are in the ratio 2 : 1 when stretched by force FA and FB respectively they get equal increase in their lengths. Then the ratio \[F_{A}\diagup F_{B}\]  should be
a) 1 : 2
b) 1 : 1
c) 2 : 1
d) 8 : 1

Answer: d

4. The breaking stress of a wire depends upon
a) Length of the wire
b) Radius of the wire
c) Material of the wire
d) Shape of the cross section

Answer: c
Explanation: Material of the wire

5. The area of cross section of a steel wire \[\left(Y=2.0\times 10^{11}N\diagup m^{2}\right)\]    is 0.1 cm2. The force required to double its length will be
a) \[2\times 10^{12}N\]
b) \[2\times 10^{11}N\]
c) \[2\times 10^{10}N\]
d) \[2\times 10^{6}N\]

Answer: d

6. A rubber cord catapult has cross-sectional area \[25 m m^{2}\] and initial length of rubber cord is 10 cm. It is stretched to 5 cm. and then released to project a missile of mass 5 gm. Taking \[Y_{rubber}=5\times 10^{8}N\diagup m^{2}\]    . velocity of projected missile is
a) \[20 ms^{-1}\]
b) \[100 ms^{-1}\]
c) \[250 ms^{-1}\]
d) \[200 ms^{-1}\]

Answer: c
Explanation: Potential energy stored in the rubber cord catapult will be converted into kinetic energy of mass.

7. According to Hook’s law force is proportional to
a) \[\frac{1}{x}\]
b) \[\frac{1}{x^{2}}\]
c) x
d) \[x^{2}\]

Answer: c
Explanation: According to Hook’s law force is proportional to x

8. In the Young’s experiment, If length of wire and radius both are doubled then the value of Y will become
a) 2 times
b) 4 times
c) Remains same
d) Half

Answer: c
Explanation: Remains same

9. Minimum and maximum values of Poisson’s ratio for a metal lies between
a) \[-\infty\] to \[+\infty\]
b) 0 to 1
c) \[-\infty\] to 1
d) 0 to 0.5

Answer: d
Explanation: 0 to 0.5

10.A wire of diameter 1mm breaks under a tension of 1000 N. Another wire, of same material as that of the first one, but of diameter 2 mm breaks under a tension of
a) 500 N
b) 1000 N
c) 10000 N
d) 4000 N

Answer: d
Explanation: Breaking force \[\propto\] r2
If diameter becomes double then breaking force will become four times i.e. 1000 × 4 = 4000 N