Direction: In the following questions, a statement of assertion (A) is...
Assertion (A) is true but reason (R) is false. (A).
Work done by a force is given by the equation: W = F * d * cos(θ), where F is the force, d is the displacement, and θ is the angle between the force and displacement vectors. The angle between the force and displacement vectors is measured in radians. The cosine of the angle is positive when the force and displacement vectors are in the same direction, and negative when they are in opposite directions. The work done by the force can be positive or negative depending on the direction of the force and displacement. If the force and displacement are in the same direction, the work done is positive and if they are in opposite direction, the work done is negative. The reason given in the statement that force is taken as positive when it acts opposite to the direction of displacement, supports the assertion that work done by the force can be positive or negative.
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Direction: In the following questions, a statement of assertion (A) is...
Assertion : Work done by the force can be positive or negative.
Reason : Force is taken as positive when it acts opposite to the direction of displacement.
The correct answer is option 'A' - Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
Explanation:
Work done is the product of force and displacement. It is a scalar quantity and can be positive, negative, or zero.
The reason provided for the assertion is correct. When the force acts opposite to the direction of displacement, the work done is negative. This is because the force is doing work against the direction of motion, resulting in a decrease in the energy of the system.
To understand this better, consider the following scenarios:
1. Positive work done:
- When the force and displacement are in the same direction, positive work is done.
- For example, if a person pushes a box in the same direction as the force applied, the work done will be positive.
2. Negative work done:
- When the force and displacement are in opposite directions, negative work is done.
- For example, if a person pulls a box backward, the work done will be negative because the force is acting opposite to the displacement.
3. Zero work done:
- When the force and displacement are perpendicular to each other, no work is done.
- For example, if a person pushes a box sideways, the force and displacement are perpendicular, resulting in zero work done.
Therefore, the assertion that work done by the force can be positive or negative is true. The reason provided, that force is taken as positive when it acts opposite to the direction of displacement, is the correct explanation for this assertion.
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