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:
\[
\boxed{0.6 \, \text{N}}
\]
