Question

Which of the following is a dimensionless quantity?
(a) Relative density
(b) Stress
(c) Heat
(d) Specific heat
Pair of quantities having same dimensional formula is
(a) Force and Work
(b) Momentum and Impulse
(c) Pressure and Force
(d) Surface tension and Stress​

Answer 1

Answer:

1. Option (a) is correct answer

2. Option (b) is correct answer

Explanation:

1. Relative Density is a Dimensionless Quantity

2. Impulse = (Change in momentum) and hence impulse and Momentum have same dimensions. [MLT-1]

Answer 2

Relative density is a dimensionless quantity (option a). Momentum and impulse have the same dimensional formula (option b).

• Relative density can be defined as the density of a substance relative to the density of a given reference substance.
• It is measured as the ratio of both the densities. And so, it is dimensionless as ration does not have any dimension.

• Momentum is the product of the mass and the velocity of a given object.
• Impulse is the product of force and time.

       i.e. F Δt = M a Δt

                     = M Δv/ Δt ×Δt

                     = M Δv (change in momentum)

• Since, impulse is the change in momentum so they have the same dimensional formula.

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