A bucket water filled upto a height = 15 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 atmospheric pressure at the bottom is

Options

A. 0.5 kPa
B. 1 kPa
C. 5kPa
D. None of these

Answer

To find the water pressure above atmospheric pressure at the bottom of the bucket, we can follow these steps:

### Step 1: Understand the System
The bucket is filled with water to a height of 15 cm. The bucket is tied to a rope that passes over a frictionless pulley, and the other end of the rope is tied to a weight that is half the mass of the bucket plus the mass of the water.

### Step 2: Define the Variables
Let:
- \( m \) = mass of the bucket + mass of the water
- \( h \) = height of the water = 15 cm = 0.15 m
- \( g \) = acceleration due to gravity = 9.81 m/s²

### Step 3: Calculate the Effective Weight
The weight acting on the system due to the mass hanging from the rope is:
\[ W = \frac{m}{2} \cdot g \]
The effective force acting on the bucket due to the weight is:
\[ F_{\text{net}} = m \cdot g - \frac{m}{2} \cdot g = \frac{m}{2} \cdot g \]

### Step 4: Calculate the Acceleration
Using Newton's second law, we can find the acceleration of the system:
\[ F_{\text{net}} = (m + \frac{m}{2}) \cdot a \]
\[ \frac{m}{2} \cdot g = \frac{3m}{2} \cdot a \]
Solving for \( a \):
\[ a = \frac{g}{3} \]

### Step 5: Determine the Pressure at the Bottom of the Bucket
The pressure at the bottom of the bucket due to the water column is given by:
\[ P = \rho \cdot g \cdot h \]
Where \( \rho \) is the density of water (approximately \( 1000 \, \text{kg/m}^3 \)). Therefore, substituting the values:
\[ P = 1000 \cdot 9.81 \cdot 0.15 \]
Calculating this gives:
\[ P = 1471.5 \, \text{Pa} \]

### Step 6: Calculate the Water Pressure Above Atmospheric Pressure
The water pressure above atmospheric pressure is:
\[ P_{\text{above}} = P - P_{\text{atmospheric}} \]
Since atmospheric pressure is not included in this calculation, we can consider the pressure calculated as the gauge pressure:
\[ P_{\text{above}} = 1471.5 \, \text{Pa} \approx 1.47 \, \text{kPa} \]

### Final Answer
The water pressure above atmospheric pressure at the bottom of the bucket is approximately **1.47 kPa**.

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