Question

Which of the following physical quantity has the dimensions [MLT^-2]?
1. Force
2. Linear momentum
3. Acceleration
4. Pressure

Answer 1

Correct Answer - Option 1 : Force

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

CONCEPT:

• Fundamental units: It includes units of mass, length, time, temperature, amount of substance, luminous intensity, and electric current.
• The dimension of a physical quantity: It is the power to which the fundamental units must be raised to represent the physical quantity.
  • For example; The dimension of mass is [M¹L⁰T⁰] and that of length is [M⁰L¹T⁰].

Newton's second law of motion:

F = mass (m) × acceleration (a)

EXPLANATION:

Since F = ma 

The mass and acceleration have the dimensions of [M¹L⁰T⁰] and [M⁰L¹T^-2] respectively, it multiplies to give the dimension of [M¹L¹T^-2].

• Hence, the force has the dimensions of [M¹L¹T^-2].

Linear Momentum(p) = m v

 where, m = mass that has dimension [M1L0T0]  and v = velocity that has dimension [M⁰L¹T^-1]. It multiplies to give [M1L¹T^-1].

​Acceleration (a) = (v- u)/t 

Where v and u are final and initial velocities respectively that have the dimension [M0L1T-1] and t=time that has dimension [M0L⁰T1]. It multiplies to give a dimensional formula of [M0L1T^-2].

• Pressure(P): The force per unit area is called pressure.

​P = F/A

where F = force that has the dimension of [M1L1T-2] and A = area that has the dimension of [M⁰L²T⁰]. It multiplies to give [M1L^-1T-2].

• Some numbers do not have any unit and are called dimensionless numbers. For example Constants such as e, π, I, coefficient of friction etc.