Question

Identify the pair of physical quantities, whose dimensions are equal *

(a) work and energy

(b) distance and displacement

(c) speed and velocity

(d) all of the above

​

Answer 1

Solution :-

1. Here work and Energy have same unit . So they have same dimension formula.
2. Distance and Displacement also similarly have same unit and hence same dimensional formula.
3. Speed and Velocity also.

Hence option d is correct

Answer 2

Given :  (a) work and energy  

(b) distance and displacement  

(c) speed and velocity

(d) all of the above

To Find :  Identify the pair of physical quantities, whose dimensions are equal  

Solution:

Work   = Force * d   = m * a * d  =  MLT⁻²L  = ML²T⁻²

Energy = mgh or  (1/2)mv²

mgh  = MLT⁻²L  = ML²T⁻²

(1/2)mv² = M ( LT⁻¹)² =  ML²T⁻²

Work   = Energy = ML²T⁻²

distance and displacement = L

speed and velocity   =  LT⁻¹

Hence all of the above have same dimension

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