In a new system of units, the unit of mass is 100 g, the unit of length is 4 m, and the unit of time is 2 s. If the numerical value of 10 J of energy in this new system is N, find the value of N/5.

Correct answer: 5

Solution

Applying dimensional analysis: 10 J = 10 kg*m²/s². In new units, 1 kg = 10 new_M, 1 m = (1/4) new_L, 1 s = (1/2) new_T. So N = 10 * 10 * (1/4)² * (2)² = 10 * 10 * (1/16) * 4 = 25, giving N/5 = 5.

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