Question

A hollow vertical cylinder of radius r and height h and has a smooth internal surface. A small particle is placed in contact with the inner side of the upper rim, at point A, and given a horizontal speed u, tangential to the rim. It leaves the lower rim at point B, at vertically below A. If n is an integer, then what is relation between u, r, h, n and g ?

Answer 1

"Vertical Speed: Kinematic expression will be:

S = ut +1/2 at^2

Put the given values,

H = 0 * t + ½ gt^2

H = ½ gt^2

T = square root of (2h/ g)    eq (1)

Horizontal Speed: = n (2 * π* r)

2nπr = ut

T = 2nπr/u   eq(2)

Equating eq(1) and eq(2) RHS,

Square root of (2h/g) = 2nπr/u

N = u [ square root (2h/g)/ 2πr]

"