Question

Figure shows an ideal spring block system, force constant of spring is k which has been compressed by an amount x0. If x is instantaneous deflection of spring from its natural length, mark the correct option (s).

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Solution

The correct option is **C** Maximum power occurs at x=x0√2

(A)−12k(x2−x20)=12mv2−0

∴v=√km(x20−x2)

∴P=F.v=kx√km(x20−x2)

(C)y=x20x2−x4

dydx=0⇒x=x0√2

∴Pmax is at x=x0√2

(B)P=k√km(x20x2−x4)

Pmax=k2√kmx20

(A)−12k(x2−x20)=12mv2−0

∴v=√km(x20−x2)

∴P=F.v=kx√km(x20−x2)

(C)y=x20x2−x4

dydx=0⇒x=x0√2

∴Pmax is at x=x0√2

(B)P=k√km(x20x2−x4)

Pmax=k2√kmx20

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