Units & Dimensions Test

Result

Units & Dimensions Test - 5

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Question 1
1 / -0

Identify the pair whose dimensions are equal.
[AIEEE 2002]

A
Torque and work

B
Stress and energy

C
Force and stress

D
Force and work

Solution

The dimensions of torque and work are [ML²T^-2]
Question 2
1 / -0

The physical quantities not having same dimensions are
[AIEEE 2003]

A
Torque and work

B
Momentum and Planck's constant

C
Stress and Young's modulus

D
Speed and (μ₀ε₀)^-1/2

Solution

Planck's constant (in term of unit)
(h) = j-s
= [ML²T^-2][T]
= [ML²T^-1]
Momentum (p) = kg-ms^-1
=[M][L][T^-1] = [MLT^-1]
Question 3
1 / -0

Which of the following is a dimensional constant?

A
e

B
Area

C
Specific gravity

D
Gravitational constant

Solution

The physical quantities which possess dimensions and have constant values are called dimensional constants. Hence Gravitational constant is a dimensional constant.
Question 4
1 / -0

Dimensions of where symbols have their usual meaning, are
[AIEEE 2003]

A
[L^-1T]

B
[L²T²]

C
[L²T^-²]

D
[LT^-¹]

Solution

As we know that formula of velocity is
Question 5
1 / -0

Which one of the following represents the correct dimensions of the coefficient of viscosity?
[AIEEE 2004]

A
[ML^-¹T^-²]

B
[MLT^-¹]

C
[ML^-1T^-1]

D
[ML^-2T^-²]

Solution

By Newton's formula
Question 6
1 / -0

The average life of an Indian is 56 years. Find the number of times the human heart beats in the life of an Indian, if the heat beats once in 0.8 s.

A
20.4×10⁹ times

B
2.5×10⁹ times

C
2.2×10⁹ times

D
6.1×10⁹ times

Solution

Average life of an Indian = 56 years = 56×3 65.25 × 24 × 60 × 60 s
Period of heart beat = 0.8 s
Total number of heartbeats in 56 years = (56 × 365.25 × 24 × 60 × 60)/0.8 = 2.2 × 10⁹ times.
Question 7
1 / -0

Out of the following pairs, which one does not have identical dimensions ?
[AIEEE 2005]

A
Angular momentum and Planck's constant

B
Impulse and momentum

C
Moment of inertia and moment of a force

D
Work and torque

Solution

I = mr²
∴[I] = [ML²]
and = moment of force =
∴ = [L][MT^-2]=[ML²T^-2]
Question 8
1 / -0

Which of the following units denotes the dimensions [ML²/Q²], where Q denotes the electric charges ?
[AIEEE 2006]

A
Wb/m²

B
Henry (H)

C
H/m²

D
Weber (Wb)

Solution

Magnetic energy
[L→ inductance, i → current]
Energy has the dimension = [ML²T^-2]
Equate the dimension, we have
Question 9
1 / -0

A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 ms^-¹. The magnitude of its momentum is recorded as
[AIEEE 2008]

A
17.6 kg ms^_1

B
17.565 kg ms^_1

C
17.56 kg ms^_1

D
17.57 kg ms^_1

Solution

m = 3.513 kg and v = 5.00 ms^-1
So momentum, p = mv = 17.565 As the number of significant digits in m is 4 and in v is 3, so p must have 3 (minimum) significant digits.
Hence, p = 17.6 kg ms^-1
Question 10
1 / -0

The dimensions of magnetic field in M, L, T and C (coulomb) is given as
[AIEEE 2008]

A
[MLT^-C^-¹]

B
[MT²C^-²]

C
[MT^-¹C^-¹]

D
[MT²C^-1]

Solution

We know that F = q v B where q is charge, v is velocity and B is magnetic field.
Hence we get B = F / q v
Therefore [B] = [F] / [q] [v]
= MLT^-2 / C.LT^-1
= MCT^-1