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

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

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.

As we know that formula of velocity is

By Newton's formula

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.

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

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

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