Question

A bucket contains water filled upto a height $=15\text{cm}$. The bucket is tied to a rope which is passed over a frictionless light pulley and the other end of the rope is tied to a weight of mass which is half of that of the (bucket + water). The water pressure above atmosphere pressure at the bottom is

• A. $0.5\text{kPa}$
• B. $1\text{kPa}$
• C. $5\text{kPa}$
• D. None

Answer 1

The correct option is B $1\text{kPa}$

Let $M$ be the mass of bucket and $T$ be the tension in the rope.
For Bucket : $Mg-T=Ma$
For the weight : $T-\frac{Mg}{2}=\frac{Ma}{2}$
Solving the two equations, $a=\frac{g}{3}$

Gauge Pressure at bottom of the bucket is $P=h\rho g_{\text{eff}}$
As bucket is accelerating down, for the water in the bucket
$g_{\text{eff}}=g-\frac{g}{3}=\frac{2g}{3}$
$\therefore P=0.15\times 1000\times \frac{2\times 10}{3}=1\text{kPa}$