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Asseration : Power of a constant force i...

Asseration : Power of a constant force is also constant.
Reason : Net constant force will always produce a constant acceleration.

A

If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.

B

If both Assertion and Reason are true and the Reason is not the correct explanation of the Assertion.

C

If Assertion is true, but the Reason is false

D

If Assertion is false but the Reason is true.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze the assertion and the reason provided: **Assertion:** Power of a constant force is also constant. **Reason:** Net constant force will always produce a constant acceleration. ### Step-by-Step Solution: 1. **Understanding Power:** - Power (P) is defined as the rate at which work is done. Mathematically, it can be expressed as: \[ P = F \cdot v \] where \( F \) is the force and \( v \) is the velocity. 2. **Constant Force and Acceleration:** - According to Newton's second law, if a constant force \( F \) is applied to an object of mass \( m \), it produces a constant acceleration \( a \): \[ F = m \cdot a \quad \Rightarrow \quad a = \frac{F}{m} \] - Since both \( F \) and \( m \) are constants, \( a \) is also constant. 3. **Velocity as a Function of Time:** - If the object starts from rest (initial velocity \( u = 0 \)), the velocity \( v \) after time \( t \) can be expressed as: \[ v = u + at = 0 + at = at \] - Substituting \( a \) in terms of \( F \): \[ v = \frac{F}{m} \cdot t \] 4. **Substituting Velocity into Power Equation:** - Now, substituting \( v \) back into the power equation: \[ P = F \cdot v = F \cdot \left(\frac{F}{m} \cdot t\right) = \frac{F^2}{m} \cdot t \] 5. **Analyzing Power Over Time:** - From the equation \( P = \frac{F^2}{m} \cdot t \), we see that power is proportional to time \( t \). As time increases, power also increases. - Therefore, the power is not constant; it varies with time. 6. **Conclusion:** - The assertion that "Power of a constant force is also constant" is **false**. - The reason that "Net constant force will always produce a constant acceleration" is **true**. ### Final Answer: - Assertion is false, Reason is true. Hence, the correct option is option 4.

To solve the question, we need to analyze the assertion and the reason provided: **Assertion:** Power of a constant force is also constant. **Reason:** Net constant force will always produce a constant acceleration. ### Step-by-Step Solution: ...
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