A thin meter scale is kept vertical by placing its one end on floor, keeping the end in contact stationary, it is allowed to fall. Calculate the velocity of its upper end when it hit the floor.

Explanation

P.E. of the metre scale in the vertical position = Rotational K.E. when the end B just touches the floor.

P.E. of metre scale `=mg. l/2` The weight of scale acts through its C. G. l = 1m
Rotational K.E. = `1/2 I omega^(2)`
M.I. of scale about one end
`mg l/2 = 1/2 I omega^(2) =1/2 (ml^(2))/3 xx v^(2)/l^(2) = (mv^(2))/6`
`v^(2) = 3gl, v= sqrt(3gl) = sqrt(3 xx 9.8 xx 1) = 5.422 ms^(-1)`