Physics : Nature of Physical World and Measurement : Book Back Choose the correct Answers with Solution, One Mark and Multiple choice questions with Answers and Solution

__Nature of Physical World and Measurement__

__Multiple Choice Questions__

1. One of the combinations from the fundamental physical constants is hc/G .

The unit of this expression is

a) Kg2

b) m 3

c) S-1

d) m

**Answer: a) kg ^{2}**

**Solution: **

Dimension for h=ML^{2}T^{-1}

c = LT^{-1}

G = M^{-1}L^{3}T^{-2}

hc / G = ([ ML^{2}T^{-1 ×} LT^{-1} ] / [
M^{-l} L^{3} T^{2} ]) M^{2} = kg^{2}

2. If the error in the measurement of radius is 2%, then the error in the determination of volume of the sphere will be

a) 8%

b) 2%

c) 4%

d) 6%

**Answer: d) 6%**

**Solution:**

volume = 4/3 πr^{3}

error = 3×2% =6%

3. If the length and time period of an oscillating pendulum have errors of 1% and 3% respectively then the error in measurement of acceleration due to gravity is

a) 4%

b) 5%

c) 6%

d) 7%

**Answer: d) 7%**

**Solution:**

4. The length of a body is measured as 3.51 m, if the accuracy is 0.01mm, then the percentage error in the measurement is

a) 351%

b) 1%

c) 0.28%

d) 0.035%

**Answer: c) 0.28%**

**Solution:**

% error = ( ∆*l / l* ) ×
100%

% error = (0.01/3.51) × 100%

= 1/3.51 = 0.28%

5. Which of the following has the highest number of significant figures?

a) 0.007 m2

b) 2.64x1024 kg

c) 0.0006032 m2

d) 6.3200 J

**Answer: d) 6.3200J**

**Solution:**

0.007 → 1

2.64 × 10^{24} →3

0.0006032 → 4

6.3200 → 5

6. If π = 3.14, then the value of π2 is

a) 9.8596

b) 9.860

c) 9.86

d) 9.9

**Answer: c) 9.86**

**Solution: **

π^{2} = 3.14 × 3.14

= 9.8596

Rounded to 3 significant fig. = 9.86

7. Which of the following pairs of physical quantities have same dimension?

a) force and power

b) torque and energy

c) torque and power

d) force and torque

**Answer: b) torque
and energy**

**Solution: **

Force = MLT^{-2}

Torque = ML^{2}T^{-2}

Energy = ML^{2}T^{-2}

Power = ML^{2}T^{-3}

8. The dimensional formula of Planck's constant h is

a) [ML2T-1]

b) [ML2T-3]

c) [MLT-1]

d) [ML3T-3]

**Answer: a) ML ^{2}T^{−1}**

**Solution:**

E = hγ

h = E/γ = [ ML^{2}T^{2} ] / T^{−1}

= ML^{2}T^{-l}

9. The velocity of a particle v at an instant t is given by v=at+bt2. The dimensions of b is

a) [L]

b) [LT-1]

c) [LT-2]

d) [LT-3]

**Answer: d) [LT ^{−3}]**

**Solution:**

v = bt^{2}

b = v/t^{2} = LT^{-1} / T^{2}

= LT^{−3}

10. The dimensional formula for gravitational constant G is

a) [ML3T-2]

b) [M-1L3T-2]

c) [M-1L-3T-2]

d) [ML-3T2]

**Answer: b) [M ^{-1}L^{3}T^{-2}]**

**Solution:**

F = Gm_{1}m_{2 }/ r^{2}

G = Fr^{2} / m_{1}.m_{2}

= [ MLT^{−2} × L^{2} ] / M^{2}

G = [M^{−1}L^{3}T^{−2}]

11. The density of a material in CGS system of units is 4 g cm-3 . In a system of units in which unit of length is 10 cm and unit of mass is 100 g, then the value of density of material will be

a) 0.04

b) 0.4

c) 40

d) 400

**Answer: c) 40**

**Solution: **

n_{1}u_{1} = n_{2}u_{2}

4 (g/cm^{2}) = n_{2} [100/(10)^{3}]

n_{2} = [4×10^{3}] / 100 = 4000/100 = 40

12. If the force is proportional to square of velocity, then the dimension of proportionality constant is

a) [MLT0]

b) [MLT-1]

c) [ML-2T]

d) [ML-1T0]

**Answer: d) ML ^{−1}T^{0}**

**Solution: **

F ∝ *v*^{2}

F = K* v*^{2}

k = F/*v*^{2}

= MLT^{-2} / (LT^{-1})^{2} = MLT^{-2}
/ L^{2}T^{-2}

= ML^{-1}T^{0}

13. The dimension of (μ0ε0)1/2 is

(a) length

(b) time

(c) velocity

(d) force

**Answer: c) velocity**

**Solution: **

c = 1 / √(μ_{0}ε_{0})

c = [μ_{0}ε_{0}]^{−1/2}

14. Planck’s constant (h), speed of light in vacuum (c) and Newton’s gravitational constant (G) are taken as three fundamental constants. Which of the following combinations of these has the dimension of length?.

Ans: a

**Answer: a) √(hG) /
C ^{3/2}**

**Solution: **

r ∝ h^{x}c^{y}G^{z}

L = (ML^{2}T^{-1}) × (LT^{-1})y(M^{-1}L^{3}T^{-2})^{z}

L = M^{x-z}L^{2x+y+3z}T^{-x-y-2z}

x−z = 0

2x+y+3z = 1

-x-y-2z=0

On solving x =1/2

y = -3/2

z = ½

L = **√(hG) / C ^{3/2}**

15. A length-scale (*l*) depends on the permittivity (*ε*) of a dielectric material, Boltzmann constant ( kB), the absolute temperature (T), the number per unit volume (n) of certain charged particles, and the charge (q) carried by each of the particles. Which of the following expression for *l* is dimensionally correct ?

Ans: b

**Answer: b) **

**Solution: **

Answers:

1) a 2) d 3) d 4) c 5) d 6) c 7) b 8) a 9) d 10) b 11) c 12) d 13) c 14) a 15) b

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