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A horizontal plank is 10.0 m long with uniform density and mass 10kg. It rests on two supports which are placed 1.0m from each end as shown in the figure. A man of mass 80kg can stand up to distance x on the plank without causing it to topple. The value of x is

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$\frac{1}{2} m$

$\frac{1}{4} m$

$\frac{3}{4} m$

$\frac{1}{8} m$

answer is A.

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Detailed Solution

Just at the time of tipping, normal reaction at I will become zero.

$Σ ($ moments of all forces about point 2 $) = 0$

$∴ w_{1} (4) = w_{2} (x)$

$x = \frac{4 w_{1}}{w_{2}} = \frac{4 (10 g)}{80 g} = \frac{1}{2} m$

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