Question

In a certain system, there are only two fundamental quantities - force and time. If their dimensions are [F] and [T] respectively, what are the dimensions of linear momentum in this system?
1. [F¹T³]
2. [F1T1]
3. [F^-1T2]
4. [F2T2]

Answer 1

Correct Answer - Option 2 : [F1T1]

The correct answer is option 2) i.e. [F 1T1]

EXPLANATION:

• Linear momentum is defined as the product of mass and velocity.
• Dimension of mass = [M]
• Dimension of velocity = [L¹T^-1]
• Thus, the dimensions of linear momentum = [M¹L1T-1]

⇒ [M1L1T-1] = [F]a [Tb]

⇒ [M1L1T-1] = [M1L1T-2]^a [T¹]^b

⇒ [M1L1T-1] = [MaLaT-2a+b]

⇒ a = 1

⇒ -2a + b = -1 ⇒ -2(1) + b = -1 ⇒ b = 1

Dimension of linear momentum = [F1T1]

​Fundamental quantity: A quantity that can be measured is called a physical quantity. 

Fundamental quantities are those which cannot be expressed or measured in terms of other physical quantities. 

The seven fundamental quantities along with their dimensions are as follows:

Fundamental quantity	Dimension
Time	T
Mass	M
Electric current	A
Thermodynamic temperature	K
Amount of substance	mol
Luminous intensity	cd
Length	L