A rod length 15 m stands vertically on the ground. With one end hinged to the ground. When it falls on the ground such that it rotates without slipping, the velocity of the upper tip on striking the ground is

Options

A. 15 m/s
B. `15 sqrt(2)m//s`
C. `15/sqrt(2)m//s`
D. `15 sqrt(3) m//s`

Answer

B

Explanation

`PE=KE_(0)`/rot

`mgh = (1)/(2)I omega^(2)`
`mgh = (1)/(2)(Ml^(2))/(3)omega^(2)`
`(gl)/(2)=(1)/(2)(l^(2)omega^(2))/(3)`
`omega^(2)=(3g)/(L)` `(V^(2))/(L^(2))=(3g)/(L)`
`V= sqrt(3gL)= sqrt(3xx10xx15)=sqrt(450)`
`= 15 sqrt(2) m//s`.