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Test: Dimensions of physical quantities , formulae and equations (April 2) - JEE MCQ


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10 Questions MCQ Test Daily Test for JEE Preparation - Test: Dimensions of physical quantities , formulae and equations (April 2)

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Test: Dimensions of physical quantities , formulae and equations (April 2) - Question 1

Identify the pair whose dimensions are equal.

[AIEEE 2002]

Detailed Solution for Test: Dimensions of physical quantities , formulae and equations (April 2) - Question 1

The dimensions of torque and work are [ML2T-2]

Test: Dimensions of physical quantities , formulae and equations (April 2) - Question 2

The physical quantities not having same dimensions are

[AIEEE 2003]

Detailed Solution for Test: Dimensions of physical quantities , formulae and equations (April 2) - Question 2

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]

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Test: Dimensions of physical quantities , formulae and equations (April 2) - Question 3

Which of the following is a dimensional constant?

Detailed Solution for Test: Dimensions of physical quantities , formulae and equations (April 2) - Question 3

A dimensional constant is a physical quantity that has a fixed numerical value and is independent of the unit system used. It represents a fundamental property of nature and remains constant regardless of the measurement units employed.

Among the options given, the gravitational constant, denoted by "G," is a dimensional constant. It is a fundamental constant in physics that appears in Newton's law of universal gravitation and describes the strength of the gravitational force between two objects.

The other options, "e" (Euler's number), area, and specific gravity, are not dimensional constants as they are dependent on the chosen unit system or can vary based on the properties of the objects or substances being measured.

Test: Dimensions of physical quantities , formulae and equations (April 2) - Question 4

Dimensions of  where symbols have their usual meaning, are

[AIEEE 2003]

Detailed Solution for Test: Dimensions of physical quantities , formulae and equations (April 2) - Question 4

As we know that formula of velocity is

Test: Dimensions of physical quantities , formulae and equations (April 2) - Question 5

Which one of the following represents the correct dimensions of the coefficient of viscosity?

 [AIEEE 2004]

Detailed Solution for Test: Dimensions of physical quantities , formulae and equations (April 2) - Question 5

By Newton's formula



Test: Dimensions of physical quantities , formulae and equations (April 2) - Question 6

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.

Detailed Solution for Test: Dimensions of physical quantities , formulae and equations (April 2) - Question 6

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.

Test: Dimensions of physical quantities , formulae and equations (April 2) - Question 7

Out of the following pairs, which one does not have identical dimensions ?

[AIEEE 2005]

Detailed Solution for Test: Dimensions of physical quantities , formulae and equations (April 2) - Question 7

I = mr2
∴[I] = [ML2]
and = moment of force = 
 = [L][MT-2]=[ML2T-2]

Test: Dimensions of physical quantities , formulae and equations (April 2) - Question 8

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

   [AIEEE 2006]

Detailed Solution for Test: Dimensions of physical quantities , formulae and equations (April 2) - Question 8

Magnetic energy 
[L→ inductance, i → current]
Energy has the dimension = [ML2T-2]
Equate the dimension, we have  

Test: Dimensions of physical quantities , formulae and equations (April 2) - Question 9

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]

Detailed Solution for Test: Dimensions of physical quantities , formulae and equations (April 2) - Question 9

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

Test: Dimensions of physical quantities , formulae and equations (April 2) - Question 10

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

[AIEEE 2008]

Detailed Solution for Test: Dimensions of physical quantities , formulae and equations (April 2) - Question 10

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