Question Detail
Question
A calorie is a unit of heat or energy and it equals about 4.2 J. Suppose we employ a system of units in which the unit of mass = α kg, length = β m, and time = γ s. Determine the magnitude of 4.2 J in terms of the new units.
Correct Answer
Option A is the correct answer.
Detailed Explanation
Energy has dimensions ML²T⁻². In new system: unit mass = α kg → 1 kg = 1/α new mass unit. Similarly, 1 m = 1/β new length unit, 1 s = 1/γ new time unit. So, 1 J = 1 kg m² s⁻² = (1/α)(1/β)²(1/γ)⁻² = α⁻¹ β⁻² γ² new energy units. Therefore, 4.2 J = 4.2 α⁻¹ β⁻² γ² in new units.
Hint
Convert the joule into the new system using dimensional analysis.