A staircase contains four steps each `10 cm` high and `20 cm` wide. The minimum horizontal velocity of a ball rolling off the uppermost plane so as to hit directly the lowest plane is

Options

A. `1 m//s`
B. `2 m//s`
C. `3 m//s`
D. `4m//s`

Answer

B

Explanation

For the minimum value of the horizontal velocity, the ball should just pass the edge of the `(n - 1)^(th)` step if it is to strike the `n^(th)` step.

`O` to `B`: `x = 2b = 2 xx 0.2 = 0.4 m`
`y = 2 h = 2 xx 0.1 = 0.2 m`
`= (g x^(2))/(2u^(2)) rArr u = sqrt((g x^(2))/(2y)) = x sqrt((g)/(2 y))`
`= (0.4)sqrt((10)/(2 xx 0.2)) = 0.4 xx 5 = 2 m//s = u_(min)`