A force \(F=F_0+\frac12kx\) (where \(x\) is the rightward displacement of the block \(A\)) acts on the block \(A\) as shown in the figure. The spring is initially unextended and the block is at rest. There is no friction anywhere. The maximum extension in the spring is:
                        
 
1. \(\dfrac{F_0}{k}\) 2. \(\dfrac{2F_0}{k}\)
3. \(\dfrac{4F_0}{k}\) 4. \(\dfrac{F_0}{2k}\)
Subtopic:  Potential Energy: Relation with Force |
Level 3: 35%-60%
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A force \(2x\hat i - 3y^2\hat j\) acts on a particle when it is at the location \(({x, y}).\) This force is:

1. non-conservative
2. conservative and the potential energy is \(({x^2-y^3})\)
3. conservative and the potential energy is \(({y^3-x^2})\)
4. conservative, but it cannot have a potential energy

Subtopic:  Potential Energy: Relation with Force |
Level 3: 35%-60%
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