Choose the correct answers

Properties of Matter (Physics)

Multiple Choice Questions

1. Consider two wires X and Y. The radius of wire X is 3 times the radius of Y. If they are stretched by the same load then the stress on Y is

(a) equal to that on X

(b) thrice that on X

(c) nine times that on X

(d) Half that on X

Answer : c) nine times that on X

Solution:

σ_x ∝ 1 / r_x² ;

σ_y ∝ 1 / r_y²

σ_x / σ_y = (r_y / r_x )² = (r_y / 3r_y )²

σ_x / σ_y = (1/3)² = 1 / 9

σ_y = 9 σ_x

2. If a wire is stretched to double of its original length, then the strain in the wire is

(a) 1

(b) 2

(c) 3

(d) 4

Answer : a) 1

Solution:

ε = Δl / l

ε = [ l_t – l_o ] / l_o

= (2 – 1) / 1 = 1 / 1 = 1

3. The load – elongation graph of three wires of the same material are shown in figure. Which of the following wire is the thickest?

(a) wire 1

(b) wire 2

(c) wire 3

(d) all of them have same thickness

Answer : a) wire 1

Solution:

If slope is high the elongation will be less

4. For a given material, the rigidity modulus is (1/3) rd of Young’s modulus. Its Poisson’s ratio is

(a) 0

(b) 0.25

(c) 0.3

(d) 0.5

Answer : d) 0.5

Solution:

η = 1/3 y

y = 2 η (1 + μ )

y = 2y/3 (1 + μ )

3/2 = 1 + μ

μ = (3/2) – 1 = 1 / 2

μ = 0.5

5. A small sphere of radius 2cm falls from rest in a viscous liquid. Heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity is proportional to

(a) 22

(b) 23

(c) 24

(d) 25

Answer : d) 2⁵

Solution:

dQ / dt = E / t = Power

Power = P = F × v_t

F = 6πηrv_t

dQ / dt = 6πηrv_t²

v_t = [2/9] [ (ρ – σ ) / η]g × [ r²]

dQ / dt = 6πηr × ( 2/9 [ (ρ–σ)/η × g ])² × r⁴

dQ / dt ∝ r⁵

6. Two wires are made of the same material and have the same volume. The area of cross sections of the first and the second wires are A and 2A respectively. If the length of the first wire is increased by ∆l on applying a force F, how much force is needed to stretch the second wire by the same amount?

(a) 2

(b) 4

(c) 8

(d) 16

Answer : b) 4 F

Solution:

y = Fl / [Δl × A]

y = [ Fl / AΔl ] × [ A / A ] = [F.V ] / [Δl × A²]

F ∝ A²

F₂ / F₁ = [ (2A)² ] / [A² ] = 4

F₂ = 4 F₁

7. With an increase in temperature, the viscosity of liquid and gas, respectively will

(a) increase and increase

(b) increase and decrease

(c) decrease and increase

(d) decrease and decrease

Answer : c) decrease and increase

8. The Young’s modulus for a perfect rigid body is

(a) 0

(b) 1

(c) 0.5

(d) infinity

Answer : d) infinity

Solution:

Y = Fl / ΔlA = Fl / [O × A] = Fl / O

Y = ∞

9. Which of the following is not a scalar?

(a) viscosity

(b) surface tension

(c) pressure

(d) stress

Answer : d) stress

10. If the temperature of the wire is increased, then the Young’s modulus will

(a) remain the same

(b) decrease

(c) increase rapidly

(d) increase by very a small amount

Answer: b) decrease

Solution:

Y = (Fl) / (A.Δt)

⇒ Y ∝ 1 / Δt 

11. Copper of fixed volume V is drawn into a wire of length l. When this wire is subjected to a constant force F, the extension produced in the wire is ∆l. If Y represents the Young’s modulus, then which of the following graphs is a straight line?

(a) ∆l verses V

(b) ∆l verses Y

(c) ∆l verses F

(d) ∆l verses  1/l

Answer: c) Δl versus F

Solution:

Y = (Fl ) / (A. Δl) = Fl / V

12. A certain number of spherical drops of a liquid of radius R coalesce to form a single drop of radius R and volume V. If T is the surface tension of the liquid, then

(d) energy is neither released nor absorbed

Answer : c) energy = 3VT [ 1/r – 1/R ] is released

13. The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?

(a) length = 200 cm, diameter = 0.5 mm

(b) length= 200 cm, diameter = 1 mm

(c) length = 200 cm, diameter = 2 mm

(d) length= 200 cm, diameter = 3 m

Answer : a) length = 200 cm, diameter = 0.5 mm

Solution:

Δl = Fl / AY = Fl / πr²Y

Δl ∝ l / r² ,

Δl ∝ l / d²

14. The wettability of a surface by a liquid depends primarily on

(a) viscosity

(b) surface tension

(c) density

(d) angle of contact between the surface and the liquid

Answer : d) angle of contact between the surface and the liquid

15. In a horizontal pipe of non-uniform cross section, water flows with a velocity of 1 m s-1 at a point where the diameter of the pipe is 20 cm. The velocity of water (m s-1) at a point where the diameter of the pipe is

(a) 8

(b) 16

(c) 24

(d) 32

Answer : b) 16

Solution:

a₁v₁ = a₂v₂

π [d₁²v₁ / 4] = π [d₂²v₂ / 4] . v²

d₂² = [v₁ / v₂ ] d₁²

= (1/1.5) × 400 × 10^-4

= 2.66 × 10^-4

d₂ = 16.3 × 10^-2

 = 16.3 cm