Question

If the dimensional formula of force is given by [M^aL^bT^c], the value of 2a² - b - c is 
1. 3
2. 2
3. 1
4. 0

Answer 1

Correct Answer - Option 1 : 3

The correct answer is option 1) i.e. 3

CONCEPT:

• The dimensional formula is used to express any physical quantity in terms of fundamental quantities.
• 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 SI system has seven fundamental quantities i.e. time, length, mass, electric current, thermodynamic temperature, amount of substance, and luminous intensity. 
• 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:

• The force acting on an object of mass (m) with an acceleration (a) is given as, Force = ma
• Dimensional formula of mass = [M1]
• Dimensional formula of acceleration (unit: m/s2) = [L1T-2]
• Therefore, the dimensional formula of force = [M1L1T-2]

⇒ a = 1, b = 1, and c = -2

⇒ 2a2 - b - c = 2(1)² - 1 - (-2) = 3