A tube filled with water and closed at both ends uniformly rotates in a horizontal plane about the `OO'` axis. The manometers `A` and `B` fixed in the tube at distances `r_(1)` and `r_(2)` from rotational axis indicate pressure `p_(1)` and `p_(2)` respectively. Determine the angular velocity `omega` of rotation of the tube.

Options

A. ` omega = sqrt((2 (p_2 - p_1))/(rho(r_2^2 -r_1^2))) `
B. `omega = sqrt((2(p_2 - p_1))/(rho(r_2^2 +r_1^2)))`
C. `omega = sqrt((2 (r_2^2 - r_1^2))/(p_1 - p_2)) `
D. `omega = (sqrt(2(p_2 - p_1)) )/ (rho r _ 1 r_2 `

Answer

A

Explanation

` P_2 - P_1 = rho g (h_2 - h _1 ) = rho g [ (omega ^ 2 r _ 2 ^2)/(2 g ) - ( omega ^ 2 r _ 1 ^ 2 )/(2 g ) ] = rho omega ^ 2 ( ( r _ 2^ 2 - r _ 1 ^ 2 )/(2 ) ) , omega = sqrt((2 (P_2 - P_1))/(rho (r_2^2- r_1^2)) `