Question

Prove that the minium velocity of a particle at the lowest point of a vertical circle for looping the loop is under root5gr where r is the radius of the circle

Answer 1

T= mgcosQ + mv.v ÷ l

To complete the circle it had to reach the top most point of circle where cosQ =180

At top most point Tmin is 0

So, mv.v÷l=mg -(1)

By energy conservation

1÷2mv.v_1÷2 mu. u+2mgl=0

v.v=u.u -4gl

Now in (1)

u.u -4gl=gl

u=root5gl