A pair of physical quantities having the same dimensional formula is :a)angular momentum and torqueb)torque and energyc)force and powerd)power and angular momentumCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

The dimensions of angular momentum are M L²T⁻¹
That of torque is M L²T⁻²
Also dimension of energy is M L²T⁻²
Where as same of force is M LT⁻²
And of power is M L²T⁻³
Thus we get torque and energy have the same dimensional formulas.

Answer

Work ;energy and torque have same dimensional formula as these are equal to force *perpendicular distance [M][L][T^-2] * [L] =[M][L^2][T^-2]

Answer

Explanation:

Dimensional formula:
The dimensional formula is a way to express the physical quantities in terms of the fundamental dimensions such as length, mass, and time. It represents the powers to which the fundamental dimensions are raised in the expression of the physical quantity.

Similar dimensional formulas:
Two physical quantities are said to have the same dimensional formula if they are expressed in terms of the same fundamental dimensions with the same powers.

Options:
a) angular momentum and torque: The dimensional formula for angular momentum is [ML^2T^-1] and the dimensional formula for torque is [ML^2T^-2]. Therefore, option a) is incorrect as they have different dimensional formulas.

b) torque and energy: The dimensional formula for torque is [ML^2T^-2] and the dimensional formula for energy is [ML^2T^-2]. Therefore, option b) is correct as they have the same dimensional formula.

c) force and power: The dimensional formula for force is [MLT^-2] and the dimensional formula for power is [ML^2T^-3]. Therefore, option c) is incorrect as they have different dimensional formulas.

d) power and angular momentum: The dimensional formula for power is [ML^2T^-3] and the dimensional formula for angular momentum is [ML^2T^-1]. Therefore, option d) is incorrect as they have different dimensional formulas.

Conclusion:
The correct answer is option b) torque and energy, as they have the same dimensional formula [ML^2T^-2].

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