A physical quantity Z is defined as the ratio of the product of impulse and linear velocit… — JAMB UTME

A physical quantity $Z$ is defined as the ratio of the product of impulse and linear velocity to the product of electric current and electric potential difference. When $Z$ is fully resolved into fundamental physical quantities, which fundamental quantity does $Z$ represent?

TimeAnswer
B
Mass
C
Length
D
Electric current

Answer

Time

The correct answer is Time because reducing both the numerator (energy) and denominator (electrical power) to base fundamental dimensions yields

\frac{M L^2 T^{-2}}{M L^2 T^{-3}} = T

, which corresponds directly to the fundamental quantity of Time.

Step-by-Step Solution

Express impulse and velocity in terms of fundamental base quantities (Mass

M

, Length

L

, Time

T

)

\text{Impulse} = \text{Force} \times \text{Time} = M L T^{-1}

\text{Velocity} = L T^{-1}

. Product

= (M L T^{-1})(L T^{-1}) = M L^2 T^{-2}

To evaluate the numerator in fundamental base dimensions.

Express electric current and potential difference in terms of fundamental base quantities

\text{Current} = I

\text{Potential Difference} = \frac{\text{Work}}{\text{Charge}} = \frac{M L^2 T^{-2}}{I T} = M L^2 T^{-3} I^{-1}

. Product

= I \times (M L^2 T^{-3} I^{-1}) = M L^2 T^{-3}

To evaluate the denominator in fundamental base dimensions.

Divide the numerator by the denominator to simplify quantity

Z

Z = \frac{M L^2 T^{-2}}{M L^2 T^{-3}} = M^{1-1} L^{2-2} T^{-2 - (-3)} = T^1

Determining the net fundamental quantity after all derived units cancel out.

Key Concept

Fundamental and Derived Quantities

Question

Answer

Step-by-Step Solution

Key Concept

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