Which of the following quantities has the dimension M^1L^2T^-2? (2019)

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Question: Which of the following quantities has the dimension M^1L^2T^-2? (2019)

Options:

Correct Answer: Work

Exam Year: 2019

Solution:

Work has the dimension M^1L^2T^-2.

Which of the following quantities has the dimension M^1L^2T^-2? (2019)

Which of the following quantities has the dimension M^1L^2T^-2? (2019)

Step 1: Understand the dimensions M, L, and T. M stands for mass, L stands for length, and T stands for time.
Step 2: Identify the dimensions given in the question: M^1L^2T^-2. This means 1 mass, 2 lengths, and -2 times.
Step 3: Recall the definition of work in physics. Work is defined as force times distance.
Step 4: Know the dimensions of force. Force is mass times acceleration. Acceleration has dimensions of L^1T^-2.
Step 5: Combine the dimensions of force and distance to find the dimensions of work. Work = Force × Distance = (M^1L^1T^-2) × (L^1) = M^1L^2T^-2.
Step 6: Conclude that work has the dimensions M^1L^2T^-2, which matches the quantity in the question.

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