Question

A rod of length L whose lower end is fixed along the horizontal plane starts to topple from the vertical position. The velocity of the upper end of the rod when it hits the ground is
A. `sqrt(3gL)`
B. `sqrt(2gL)`
C. `sqrt(gL)`
D. `sqrt(5gL)`

Answer 1

Correct Answer - A
Decrease in gravitational potential energy = Increase in rotational kinetic energy about point O

or `"mg"(L)/(2)=(1)/(2)((mL^(2))/(3))omega^(2)or omega=sqrt((3g)/(L))`
Now `v = r omega` (in pure rotation)
`:. v=Lsqrt((3g)/(L))=sqrt(3gL)`.