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Question

A uniform rod AB,4m long and weight 12kg, is supported at end A, with a 6kg lead weight at B. The rod floats as shown in figure with one-half of its length submerged. The buoyant force on the lead mass is negligible as it is of negligible volume. Find the tension in the cord and the total volume of the rod.


A
10 N,32×103 m3
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B
20 N,32×103 m3
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C
20 N,16×103 m3
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D
10 N,16×103 m3
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Solution

The correct option is B 20 N,32×103 m3
Balancing forces
T+U=60+W.....(i)


(Moments) about = 0
U(l4)+T(l)=W(l2)
or U+4T=2W....(ii)
W=120 N....(iii)
Solving these three equations we get T=20 N and U=160 N
Now, 160=(V2)ρwg=(V2)(1000)(10)
V=32×103 m3

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