A) Inversely proportional to \[\left( v \right)\]
B) Proportional to \[\left( F \right)\]
C) Proportional to \[F{{v}^{-2}}\]
D) Constant
Correct Answer: C
Solution :
Key Idea : Conservative force can be represented by potential energy function. If a force acting on an object is a function of position only, it is said to be a conservative force and it can be represented by a potential energy function and which for a one dimensional case satisfies the derivative condition. \[\Rightarrow \] Given, \[F=\frac{mg\left( h+d \right)}{d}\] \[F=mg\left( 1+\frac{h}{d} \right)\] \[\Delta \,m\] \[\Delta \,E\] \[\Delta \,E=\left( \Delta \,\,m \right){{c}^{2}}\] \[\therefore \] \[=\frac{\text{Dimension of energy}}{{{\left( \text{Dimension of velocity} \right)}^{2}}}\] Hence, magnitude of force is proportional to \[\text{Energy}=\left[ ML{{T}^{-2}}\,\,L \right]=\left[ M{{L}^{2}}\,\,{{T}^{-2}} \right]\].
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