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

Options

A. `(1)/(2) m`
B. `(1)/(4) m`
C. `(3)/(4) m`
D. `(1)/(8) m`

Answer

A

Explanation

just at the time of tipping , normal reation at `1` will become zero
`sum`(moments of all forces about point `2) = 0`

`:. W_(1) (4) = w_(2) (x)`
or `x = (4 w_(1))/(w_(2)) = (4 (10 g))/(80 g) = (1)/(2) m`