Question

If in a new system of units, one unit of mass=2 Kg one unit of length=5 m and time=20 s, then find the value of 100 watt power. (dimensional analysis)

Answer 1

Answer :

In a new system of units :

• one unit of mass = 2kg
• one unit of length = 5m
• one unit of time = 20s

We have to find the value of 100W power in this new system of units$.$

Concept : We know that magnitude of physical quantity is inversely proportional to the unit of quantity.

• n ∝ 1 / u

Hence, product of magnitude and unit remains constant in any system of units.

• n₁u₁ = n₂u₂

Dimention formula of power :

• [M¹L²Tˉ³]

⇒ n₁u₁ = n₂u₂

⇒ n₂ = n₁ × (u₁ / u₂)

⇒ n₂ = n₁ × [M₁/M₂]¹ [L₁/L₂]² [T₁/T₂]ˉ³

⇒ n₂ = 100 × [1/2]¹ [1/5]² [1/20]ˉ³

⇒ n₂ = 100 × 20³/(2×25)

⇒ n₂ = 2 × 8000

⇒ n₂ = 16000 unit