Question

In a certain system of units, force (F), acceleration (A) and time (T) are the fundamentals units. Then the dimensional formula of power will be- 
1. [F¹A¹T²]
2. [F1A1T1]
3. [F1A2T1]
4. [F^-1A2T1]

Answer 1

Correct Answer - Option 2 : [F1A1T1]

The correct answer is option 2) i.e. [F1A1T1]

CONCEPT:

• ​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

EXPLANATION:

• Power is defined as the work done per unit time. 
• Dimensions of work done = force × displacement = [M¹L¹T^-2] × [L¹] = [M1L2T-2] 
• Dimensions of time = [T¹]
• Thus, the dimensions of power = [M1L2T-2] × [T1]^-1 = [M1L2T-3] 

​⇒ Power = [F^aA^bT^c]

⇒ [M1L2T-3] = [M1L1T-2]^a [L1T-2]^b  [T1]^c

⇒ [M1L2T-3] = [MaLa+bT-2a-2b+c]

⇒ a = 1 

⇒ a+b = 2 ⇒ b = 1

⇒ -2a-2b+c = -3 ⇒ -2(1)-2(1)+c = -3 ⇒ c = 1

Dimensions of power = [FaAbTc] = [F1A1T1]