Question

Find the dimensions of
(a) linear momentum,
(b) frequency and
(c) pressure.

Concept of Physics - 1 , HC VERMA , Chapter "Introduction to Physics".

Answer 1

Hello Dear.

(a)
Formula of Linear Momentum is given by →

p = m × v
where, p = Linear momentum, m = mass and v = velocity.

Now, Dimension of Mass = M L⁰ T⁰
& Dimension of Velocity = M⁰L¹T⁻¹

∴ [p] = (M¹ × 1 × 1) × (1 × L¹ × T⁻¹)  
    [ ∵ a⁰ = 1]

⇒ [p] = M¹ L¹ T⁻¹


Hence, Dimension of the Linear Momentum is M¹L¹ T⁻¹.

______________________


(b) ∵ Frequency = 1/Time
∴ [f] = 1/T
⇒ [f] = T⁻¹

Hence, the Dimension of the Frequency is M⁰ L⁰ T⁻¹.

______________________


(c) ∵ Pressure = Force/Area

Dimension of Force = M¹ L¹ T⁻²
& Dimension of Area = M⁰ L² T⁰
   = L²

∴ [P] = (M¹ L¹ T⁻²) ÷ (L²)
⇒ [P] = M¹ L⁻¹ T⁻²


Hope it helps.