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STATEMENT-1: If a spring is elongated it...

STATEMENT-1: If a spring is elongated it does positive work
STATEMENT-2: If a spring is compressed it foes negative work
STATEMENT-3: Spring does not work whether it is elongated or compressed as it is non-living

A

T T F

B

T F F

C

F T T

D

F T F

Text Solution

AI Generated Solution

The correct Answer is:
To analyze the statements regarding the work done by a spring, let's go through each statement step by step. ### Step 1: Analyze Statement 1 **Statement 1:** If a spring is elongated, it does positive work. - When a spring is elongated, it is being stretched from its equilibrium position. The restoring force exerted by the spring acts in the opposite direction to the elongation. - The work done by the spring can be calculated using the formula: \[ W = F \cdot d \cdot \cos(\theta) \] where \(F\) is the force exerted by the spring, \(d\) is the displacement, and \(\theta\) is the angle between the force and the displacement. - In the case of elongation, the angle \(\theta\) is 180 degrees (force is opposite to displacement), thus: \[ W = F \cdot d \cdot \cos(180^\circ) = -F \cdot d \] - Therefore, the work done by the spring when elongated is negative. **Conclusion:** Statement 1 is **false**. ### Step 2: Analyze Statement 2 **Statement 2:** If a spring is compressed, it does negative work. - When a spring is compressed, it is being pushed towards its equilibrium position. Again, the restoring force acts in the opposite direction to the compression. - Similar to elongation, we can use the work formula: \[ W = F \cdot d \cdot \cos(\theta) \] - In this case, the angle \(\theta\) is also 180 degrees (force is opposite to displacement), thus: \[ W = F \cdot d \cdot \cos(180^\circ) = -F \cdot d \] - Therefore, the work done by the spring when compressed is also negative. **Conclusion:** Statement 2 is **true**. ### Step 3: Analyze Statement 3 **Statement 3:** Spring does not work whether it is elongated or compressed as it is non-living. - The term "work" in physics refers to the energy transferred when a force is applied over a distance. It is not dependent on whether the object (in this case, the spring) is living or non-living. - Springs can do work when they are either compressed or elongated, as they exert forces that can result in energy transfer. **Conclusion:** Statement 3 is **false**. ### Final Conclusion - Statement 1: **False** - Statement 2: **True** - Statement 3: **False** Thus, the correct option is that Statement 2 is true while Statements 1 and 3 are false. ---
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