A steel scale measures the length of a copper wire as 80.0 cm whe

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 Multiple Choice QuestionsMultiple Choice Questions

91.

A bob of mass 10 kg is attached to wire 0.3 m long. Its breaking stress is 4.8 x107 N/m2. The area of cross-section of the wire is 10-6 m2. The maximum angular velocity with which it can be rotated in a horizontal circle is

  • 8 rad/s

  • 4 rad/s

  • 2 rad/s

  • 1 rad/s


92.

A rubber cord 10 m long is suspended vertically. How much does it stretch under its own weight? (Density of rubber is 1500 kg/m3, Y = 5 × 108 N/m2, g = 10 m/s2)

  • 15 × 10-4 m

  • 7.5 × 10-4 m

  • 12 × 10-4 m

  • 25 × 10-4 m


93.

A brass rod of cross-sectional area 1 cm2 and length 0.2 m is compressed lengthwise by a weight of 5 kg of Young's modulus of elasticity of brass is 1 x 1011 N/m2 and g = 10 m/s2, then increase in the energy of the rod will be

  • 10-5 J

  • 2.5 × 10-5 J

  • 5 × 10-5 J

  • 2.5 × 10-4 J


94.

A wire fixed at the upper end stretches by length Δl by applying a force F. The work done in stretching is

  • F2Δl

  • FΔl

  • 2 FΔl

  • FΔl2


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95.

The Young's modulus of a wire is numerically equal to the stress which will

  • not change the length of the wire

  • double the length of the wire

  • increase the length

  • change the radius of the wire to half


96.

A one-metre long steel wire of cross-sectional area 1mm2 is extended by 1 mm. If Y=2 x 1011 N/m2, then the work done is :

  • 0.1 J

  • 0.2 J

  • 0.3 J

  • 0.4 J


97.

A 5m aluminium wire (Y = 7 × 1010 N/m2) of diameter 3mm supports a 40 kg mass. In order to have the same elongation in copper wire (Y =12 x 1010 N/m2) of the same length under the same weight, the diameter should be in mm :

  • 1.75

  • 2.0

  • 2.3

  • 5.0


98.

Minimum and maximum values of Poisson's ratio for a metal lies between:

  • - ∞ to + ∞ 

  • 0 to 1

  • - ∞ to 1

  • 0 to 0.5


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99.

A wire of diameter 1 mm 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 :

  • 500 N

  • 100 N

  • 1000 N

  • 4000 N


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100.

A steel scale measures the length of a copper wire as 80.0 cm when both are at 20°C, the calibration temperature for the scale. What would the scale read for the length of the wire when both are at 40°C?

Given : α for steel = 11 × 10-6 per °C and for Cu= 17 × 10-6 per °C :

  • 80.0096 cm

  • 80.0272

  • 1 cm

  • 25.2 cm


A.

80.0096 cm

Using the relation

Increase in length of scale

lt = l0(1 + αt)

= 1 × [1 + 11×10-6 ×(40 - 20)]

= 1.00022 cm

Now, length of copper rod at 40°C

l't = l'0(1 + α't)

= 80[1 + 17×10-6 ×(40 - 20)]

= 80.0272 cm

Now, number of cms observed on the scale

= 80.02721.00022 = 80.0096


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