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A ball of mass m is suspended from the ceiling with the help of an elastic cord. An additional downward force applied on the ball, if increased gradually to a value $F_{0}$ , the cord would break. What should be the additional minimum constant force F that will break the cord ?

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$F = \frac{1}{2} F_{0}$

$F = \frac{1}{2} (F_{0} - mg)$

$F = \frac{1}{2} (F_{0} + mg)$

$F = \frac{1}{2} F_{0} + mg$

answer is A.

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Detailed Solution

$\begin{array}{l} F_{0} = {kx}_{0} \\ \Rightarrow x_{0} = \frac{F_{0}}{k} : displacement from mean position \end{array}$

$For minimum value of F$

$\begin{array}{l} W_{F} = ΔU + Δk; ΔU = {ΔU}_{e} + {ΔU}_{g} \\ \Rightarrow {Fx}_{0} = \frac{1}{2} {kx}_{0}^{2} \Rightarrow F = \frac{{kx}_{0}}{2} = \frac{F_{0}}{2} \end{array}$

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