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Assertion: Both velocity and pseed have ...

Assertion: Both velocity and pseed have same dimesions.
Reason: Velocity cannot be added to speed.

A

if both assertion and reason are true reason is the correct explanation of assertion.

B

If both assertion and reason are true but reason is not the correct explanation fo assertion.

C

If assertion is true but reaso is false.

D

IF both assertion and reason are false.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze both the assertion and the reason provided. ### Step 1: Analyze the Assertion The assertion states that "Both velocity and speed have the same dimensions." - **Definition of Velocity**: Velocity is defined as the rate of change of displacement with respect to time. Mathematically, it can be expressed as: \[ \text{Velocity} = \frac{\text{Displacement}}{\text{Time}} = \frac{L}{T} \] where \(L\) is the dimension of length and \(T\) is the dimension of time. - **Dimension of Velocity**: Therefore, the dimension of velocity is: \[ [V] = LT^{-1} \] - **Definition of Speed**: Speed is defined as the rate of change of distance with respect to time. Mathematically, it can be expressed as: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{L}{T} \] - **Dimension of Speed**: Thus, the dimension of speed is also: \[ [S] = LT^{-1} \] Since both velocity and speed have the same dimensions of \(LT^{-1}\), the assertion is **true**. ### Step 2: Analyze the Reason The reason states that "Velocity cannot be added to speed." - **Nature of Velocity and Speed**: Velocity is a vector quantity, which means it has both magnitude and direction. Speed, on the other hand, is a scalar quantity, which means it only has magnitude and no direction. - **Addition of Quantities**: In physics, vector quantities cannot be directly added to scalar quantities. Therefore, it is correct to say that velocity cannot be added to speed. Since this statement is also **true**, we conclude that both the assertion and the reason are correct. ### Step 3: Determine the Relationship However, the reason provided does not correctly explain the assertion. The assertion is about the dimensions of velocity and speed, while the reason discusses the nature of these quantities (vector vs. scalar) and their addition. ### Final Conclusion Both the assertion and reason are true, but the reason is not the correct explanation of the assertion. ### Answer - **Assertion**: True - **Reason**: True - **Conclusion**: The correct answer is that both assertion and reason are true, but the reason is not the correct explanation of the assertion. ---
To solve the question, we need to analyze both the assertion and the reason provided. ### Step 1: Analyze the Assertion The assertion states that "Both velocity and speed have the same dimensions." - **Definition of Velocity**: Velocity is defined as the rate of change of displacement with respect to time. Mathematically, it can be expressed as: \[ \text{Velocity} = \frac{\text{Displacement}}{\text{Time}} = \frac{L}{T} ...
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