1
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Question

# A channel 27 m wide falls at a right angle to another channel 64 m wide. The greatest length of a log that can be floated along this system of channel is

A
110
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B
125
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C
100
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D
120
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Solution

## The correct option is B 125From figure it clear that the length of the log l=27secθ+64cosec θ ⇒ dℓdθ=27secθtanθ−64cosecθcotθ =27sin3θ−64cos3θsinθcosθ For maximum or minimum value of l,dθ=0 ⇒ tan3θ=6427=4333 ⇒ tanθ=43 ⇒ sinθ4=cosθ3=15 ⇒ sinθ=45,cosθ=35. Clearly, d2ℓdθ2<0 for tanθ=43 Hence maximum (l)=27×53+64×54=125 m

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