Properties of Bulk Matter

Question 1

The temperature of a metallic sphere of radius R is increased by a small amount ΔT. If the linear coefficient of thermal expansion of the metal is α, the approximate increase in the volume of the sphere is:

Accepted Answer

4πR³αΔT. For small changes the fractional volume change is three times the fractional linear change: ΔV/V = 3ΔR/R = 3αΔT. With V = (4/3)πR³ this gives ΔV = 3αΔT × (4/3)πR³ = 4πR³αΔT.

Answer

2πR³αΔT

Answer

3πR³αΔT

Answer

6πR³αΔT

Question 2

A thin flat circular disc of radius 4.5 cm is placed gently over the surface of water. If the surface tension of water is 0.07 N m⁻¹, then the excess force required to take it away from the surface is

Accepted Answer

19.8 mN. The surface tension acts along the circumference of the disc, so the extra force needed is F = T × 2πr = 0.07 × 2 × 3.14 × 0.045 ≈ 0.0198 N, that is 19.8 mN. Note the circumference and not the area is what matters, and the answer is in millinewtons — the two large distractors come from using the wrong length or dropping the metre-to-centimetre conversion.

Answer

198 N

Answer

1.98 mN

Answer

99 N

Question 3

The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young’s modulus are 8 × 10⁸ N m⁻² and 2 × 10¹¹ N m⁻² respectively is

Accepted Answer

4 mm. Young’s modulus Y = stress/strain, so the maximum strain is the elastic limit divided by Y: 8 × 10⁸ / 2 × 10¹¹ = 4 × 10⁻³. The elongation is that strain times the original length, 4 × 10⁻³ × 1 m = 4 × 10⁻³ m, which is 4 mm. Beyond this the wire would no longer return to its original length.

Answer

0.4 mm

Answer

40 mm

Answer

8 mm

Q1.The temperature of a metallic sphere of radius R is increased by a small amount ΔT. If the linear coefficient of thermal expansion of the metal is α, the approximate increase in the volume of the sphere is:

Q2.A thin flat circular disc of radius 4.5 cm is placed gently over the surface of water. If the surface tension of water is 0.07 N m⁻¹, then the excess force required to take it away from the surface is

Q3.The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young’s modulus are 8 × 10⁸ N m⁻² and 2 × 10¹¹ N m⁻² respectively is