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

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

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

A wire fixed at the upper end stretches by length $\mathrm{\Delta l}$ by applying a force F. The work done in stretching is

• $\frac{\mathrm{F}}{2\mathrm{\Delta l}}$

• FΔl

• 2 FΔl

• $\frac{\mathrm{F\Delta l}}{2}$

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

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

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

• - ∞ to + ∞ 

• 0 to 1

• - ∞ to 1

• 0 to 0.5

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

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