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Hello friends, today we are going to solve this problem.
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In this question, the question says, a uniform cylinder of length l and mass m having cross -sectional area a is suspended with its length with its length vertical from a fixed point by a massless spring of constant k.
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Now, it is suspended in such a way that it is half submerged and there is a liquid of density row in the equilibrium position.
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The extension of the spring x not will have to be find out.
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Now if i write that x not has to be find out, then firstly we need a figure for this problem.
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Now the figure will look like this.
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In this figure, as you can see, there is such a diagram.
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Now let us see how we can solve this particular problem.
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First of all, i can write that let x not equals extension in equilibrium position, right? so extension if i write now this extension is in equilibrium position further of it i can say that f will be equals to restoring force in the spring so restoring force in the string okay, now what will happen? i can write for the f part as f equals kx not okay now i can write that net external so net external downward force acting on the cylinder i can write net force and that to down downward force okay now this much force acting on the cylinder will be equals to how much will it be it will be equals to m g minus up thrust so okay up thrust so this will have some value and we will look at those values what they come now mg minus l over 2 multiplied a multiplied row multiplied g so this value is here then what will happen i can just write these values for equilibrium so i can write here that for equilibrium equilibrium equilibrium k x not okay so kx0 let me just complete this statement k x not equals m g minus l a sigma g over 2 now this value will be equals to how much it will it be? it will be equals kx not equals mg...