Question:
The dimensional formula for the rate of change of momentum of a moving body is
The dimensional formula for the rate of change of momentum of a moving body is
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Always remember that "rate of change of" means dividing by time. Momentum has dimensions $[MLT^{-1}]$. Dividing by time $[T]$ immediately gives $[MLT^{-2}]$, which is the standard dimension for any type of Force.
Updated On: Apr 24, 2026
- $ML^{2}T^{-2}$
- $MLT^{-1}$
- $ML^{-1}T^{-1}$
- $MLT^{-2}$
- $M^{0}LT^{-1}$
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The Correct Option is D
Solution and Explanation
Concept:
Physics - Dimensions and Newton's Second Law.
Step 1: Relate rate of change of momentum to force.
According to Newton's Second Law of Motion, the rate of change of momentum of a body is equal to the net force acting on it. $$ F = \frac{dp}{dt} $$
Step 2: Determine the formula for force.
Force is defined as the product of mass ($m$) and acceleration ($a$): $$ F = m \times a $$
Step 3: Identify basic dimensions.
Step 4: Combine dimensions to find the final formula.
Multiply the dimensions of mass and acceleration: $$ [F] = [M] \times [LT^{-2}] $$ $$ [F] = [MLT^{-2}] $$
Physics - Dimensions and Newton's Second Law.
Step 1: Relate rate of change of momentum to force.
According to Newton's Second Law of Motion, the rate of change of momentum of a body is equal to the net force acting on it. $$ F = \frac{dp}{dt} $$
Step 2: Determine the formula for force.
Force is defined as the product of mass ($m$) and acceleration ($a$): $$ F = m \times a $$
Step 3: Identify basic dimensions.
- Dimension of Mass ($m$) = $[M]$
- Dimension of Acceleration ($a$) = $[LT^{-2}]$
Step 4: Combine dimensions to find the final formula.
Multiply the dimensions of mass and acceleration: $$ [F] = [M] \times [LT^{-2}] $$ $$ [F] = [MLT^{-2}] $$
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