A body of mass 100 gram is tied at the end of a string of length 1m. It is rotated in a vertical circle at a critical speed of 4 m/s at the highest point . The tension in the string at the huighest point in its path is [ take `g=10 m//s^(2)`]

Options

A. `0.3N`
B. `0.6N`
C. `0.9N`
D. `1.2N`

Explanation

To find the tension in the string at the highest point of the vertical circular motion, we can follow these steps:

### Step 1: Identify the given values
- Mass of the body, \( m = 100 \, \text{grams} = 0.1 \, \text{kg} \) (since \( 1 \, \text{kg} = 1000 \, \text{grams} \))
- Length of the string (radius of the circle), \( r = 1 \, \text{m} \)
- Critical speed at the highest point, \( v = 4 \, \text{m/s} \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \)

### Step 2: Write the equation for forces at the highest point
At the highest point of the vertical circle, the forces acting on the body are:
- The gravitational force acting downward, \( mg \)
- The tension in the string acting upward, \( T \)

Using Newton's second law, we can set up the equation:
\[ T + mg = \frac{mv^2}{r} \]
Where:
- \( T \) is the tension in the string
- \( \frac{mv^2}{r} \) is the centripetal force required to keep the body moving in a circle

### Step 3: Rearrange the equation to find tension
Rearranging the equation gives:
\[ T = \frac{mv^2}{r} - mg \]

### Step 4: Substitute the known values into the equation
Now, substitute the values into the equation:
- \( m = 0.1 \, \text{kg} \)
- \( v = 4 \, \text{m/s} \)
- \( r = 1 \, \text{m} \)
- \( g = 10 \, \text{m/s}^2 \)

Substituting these values gives:
\[ T = \frac{(0.1)(4^2)}{1} - (0.1)(10) \]

### Step 5: Calculate the centripetal force and gravitational force
Calculating \( \frac{mv^2}{r} \):
\[ \frac{(0.1)(16)}{1} = 1.6 \, \text{N} \]
Calculating \( mg \):
\[ (0.1)(10) = 1.0 \, \text{N} \]

### Step 6: Substitute these results back into the tension equation
Now substituting these results back into the equation for tension:
\[ T = 1.6 - 1.0 = 0.6 \, \text{N} \]

### Final Answer
The tension in the string at the highest point in its path is:
\[ \boxed{0.6 \, \text{N}} \]