Which of the following is the correct dimensional formula for acceleration? (202

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Question: Which of the following is the correct dimensional formula for acceleration? (2022)

Options:

Correct Answer: [M^0 L^1 T^-2]

Exam Year: 2022

Solution:

Acceleration is defined as the change in velocity per unit time, so its dimensional formula is [M^0 L^1 T^-2].

Which of the following is the correct dimensional formula for acceleration? (2022)

Which of the following is the correct dimensional formula for acceleration? (2022)

Step 1: Understand what acceleration is. Acceleration measures how quickly an object's velocity changes over time.
Step 2: Recall the formula for acceleration: Acceleration = Change in Velocity / Time.
Step 3: Identify the dimensions of velocity. Velocity is distance (length) divided by time, so its dimensional formula is [M^0 L^1 T^-1].
Step 4: Since acceleration is the change in velocity per unit time, we need to divide the dimensional formula of velocity by time.
Step 5: The dimensional formula for time is [M^0 L^0 T^1].
Step 6: To find the dimensional formula for acceleration, we take the dimensional formula of velocity [M^0 L^1 T^-1] and divide it by the dimensional formula of time [M^0 L^0 T^1].
Step 7: When dividing, we subtract the exponents of the same base: [M^0 L^1 T^-1] / [M^0 L^0 T^1] = [M^(0-0) L^(1-0) T^(-1-1)] = [M^0 L^1 T^-2].
Step 8: Therefore, the correct dimensional formula for acceleration is [M^0 L^1 T^-2].

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