$\"\"$

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From the given information, consider $\"\"$ .

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$\"\"$

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$\"\"$ .

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Derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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Again derivative on each side with respect to $\"\"$ .

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$\"\"$

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From the figure $\"\"$ and $\"\"$ .

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Substitute the values of $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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Equate derivative to zero.

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$\"\"$

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$\"\"$ .

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$\"\"$

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From the figure :

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$ .

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$\"\"$

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The minimum force is $\"\"$ and the angle $\"\"$ .