The coefficient of friction between a hemispherical bowl and an insect is `sqrt(0.44)` and the radius of the bowl is `0.6m`. The maximum height to which an insect can crawl in the bowl will be .

Options

A. `0.4m`
B. `0.2m`
C. `0.3m`
D. `0.1m`

Explanation

To find the maximum height to which an insect can crawl in a hemispherical bowl, we can follow these steps:

### Step 1: Determine the coefficient of friction
Given that the coefficient of friction \( \mu = \sqrt{0.44} \).

### Step 2: Calculate the angle of repose
The angle of repose \( \theta \) can be calculated using the formula:
\[ \tan \theta = \frac{1}{\mu} \]
Substituting the value of \( \mu \):
\[ \tan \theta = \frac{1}{\sqrt{0.44}} \]

### Step 3: Calculate \( \sin \theta \)
Using the identity \( \sin^2 \theta + \cos^2 \theta = 1 \) and the relationship \( \tan \theta = \frac{\sin \theta}{\cos \theta} \), we can express \( \sin \theta \) in terms of \( \mu \):
\[ \sin \theta = \frac{\mu}{\sqrt{1 + \mu^2}} \]
Substituting \( \mu = \sqrt{0.44} \):
\[ \sin \theta = \frac{\sqrt{0.44}}{\sqrt{1 + 0.44}} = \frac{\sqrt{0.44}}{\sqrt{1.44}} = \frac{\sqrt{0.44}}{1.2} \]

### Step 4: Calculate the height
The maximum height \( h \) to which the insect can crawl is given by:
\[ h = r - r \sin \theta \]
Where \( r \) is the radius of the bowl (0.6 m). Thus:
\[ h = r(1 - \sin \theta) = 0.6(1 - \frac{\sqrt{0.44}}{1.2}) \]

### Step 5: Simplify the expression
Calculating \( \sqrt{0.44} \):
\[ \sqrt{0.44} \approx 0.6633 \]
Now substituting back:
\[ h = 0.6 \left( 1 - \frac{0.6633}{1.2} \right) = 0.6 \left( 1 - 0.55275 \right) = 0.6 \times 0.44725 \approx 0.26835 \]

### Step 6: Final calculation
Thus, the maximum height \( h \) is approximately:
\[ h \approx 0.26835 \text{ m} \]

### Conclusion
The maximum height to which the insect can crawl in the bowl is approximately \( 0.26835 \text{ m} \).