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Question

A uniform rod is 4 m long and weight 10 Kg. If it is supported on a knife edge at one metre from the end, what weight placed at that end keeps the rod horizontal?

A
8 N
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B
10 N
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C
12 N
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D
15 N
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Solution

The correct option is C 10 N

Linear density of rod, μ=ML=104=2.5kgm1

Weight, W

WAB=μ×1=2.5kg

WBC=μ×3=2.5×3=7.5kg

Center of mass of AB from knife is 0.5m

Center of mass of BC from knife is 1.5m

Length of AB is short, so force apply at point A to balance the rod

Moment at point B

F×LAB=WBC×1.5WAB×0.5

F=WBC×1.5WAB×0.5LAB=7.5×1.5+2.5×0.51

F=10N

Weight placed at end of rod is 10N


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