The variation of gauge pressure ( P ) with depth ( h ) for two different liquids A and B is plotted on a graph. The straight line for liquid A makes an angle of 60^ with the h -axis, while the line for liquid B makes an angle of 30^ with the h -axis. What is the ratio of the density of liquid A to that of liquid B?

Step-by-step solution

Gauge pressure at a depth h in a liquid of density is given by P = gh . Rearranging this equation, we get P h = g . On a graph of P (y-axis) versus h (x-axis), the slope of the line is equal to P h . Therefore, the slope is directly proportional to the density of the liquid ( Slope = g ). For liquid A, the slope is (60^ ) = 3 . For liquid B, the slope is (30^ ) = 1 3 . The ratio of their densities is: _A _B = Slope _A Slope _B = (60^ ) (30^ ) = 3 1 3 = 3 Thus, the ratio of the density of liquid A to liquid B is 3:1