Question

1.Which of the following pairs of physical quantities have the same dimensions?  (speed and velocity, distance and velocity,speed and velocity, accelerationand velocity)*​

Answer 1

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Answer 2

Ques. Which of the following pairs of physical quantities have the same dimensions?

(a) speed and displacement

(b) distance and velocity

(c) speed and velocity

(d) acceleration and velocity ​

Answer:

The option (c) speed and velocity is the correct answer.

Explanation:

Speed and velocity share the same dimension since they both indicate how fast an object is travelling. Velocity is a vector variable that also indicates the object's direction of motion.

Speed: The distance an object travels at a specific time is its speed. The dimensional formula for it is $[LT^{-1} ]$. having inverted time and length dimensions as a result

Velocity: The dimensional formula for velocity is the same as that for speed $[LT^{-1} ]$ with direction because velocity is a change in distance over time.

Displacement: The formula for displacement's dimensions is $[L]$.

Acceleration: The dimensionless formula for acceleration is $[LT^{-2} ]$, where acceleration is defined as a change in velocity over time.

Thus, option c. Speed and velocity have the same dimensions.

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