A rectangular vessel is of 2m long, 0.5m breadth, and 1m deep. If water flows in at the rate of 90 cubic cm per sec, then the rate of increase of water level when 25cm deep is

• A. 0.09 cm/sec
• B. 0.1 cm/sec
• C. 0.01 cm/sec
• D. 0.5 cm/sec

To find the rate of increase of the water level in the rectangular vessel, we first need to calculate the volume of water that corresponds to a certain height. The dimensions of the vessel are:

• Length = 2 m
• Breadth = 0.5 m
• Depth = 1 m

Next, we convert the dimensions into centimeters for consistency, since the water flow rate is given in cubic centimeters:

• Length = 200 cm
• Breadth = 50 cm
• Depth = 100 cm

The cross-sectional area (A) of the vessel is:

A = Length × Breadth = 200 cm × 50 cm = 10,000 cm²

Now, we know that water flows in at a rate of 90 cm³/sec. To find the rate of increase of the water level (h) when the water is 25 cm deep, we can use the formula:

Rate of increase of water level = Flow rate / Cross-sectional area

Substituting the values:

Rate of increase of water level = 90 cm³/sec / 10,000 cm² = 0.009 cm/sec

Since we need the rate when the water is 25 cm deep, we can confirm that the rate remains constant regardless of the depth, as long as the vessel is not full. Thus, the rate of increase of the water level is:

0.009 cm/sec

However, this value is not directly listed in the options. To match the closest option, we can express it as:

0.01 cm/sec

Therefore, the correct answer is:

C. 0.01 cm/sec