Find the maximum possible percentage error in the measurement of force on an object (of mass m) travelling at velocity v in a circle of radius r if m =`(4.0 pm 0.1)`kg, v= `(10pm0.1)` m/s and r=`(8.0 pm 0.2)` m

Answer

To find the maximum possible percentage error in the measurement of force on an object of mass \( m \) traveling at velocity \( v \) in a circle of radius \( r \), we will follow these steps:

### Step 1: Identify the formula for force
The centripetal force \( F \) acting on an object moving in a circle is given by the formula:
\[ F = \frac{mv^2}{r} \]
where:
- \( m \) is the mass,
- \( v \) is the velocity,
- \( r \) is the radius.

### Step 2: Determine the percentage errors for each variable
We need to calculate the percentage errors for mass \( m \), velocity \( v \), and radius \( r \).

1. **Percentage error in mass \( m \)**:
\[ \text{Percentage error in } m = \left( \frac{\Delta m}{m} \right) \times 100 = \left( \frac{0.1}{4.0} \right) \times 100 = 2.5\% \]

2. **Percentage error in velocity \( v \)**:
\[ \text{Percentage error in } v = \left( \frac{\Delta v}{v} \right) \times 100 = \left( \frac{0.1}{10} \right) \times 100 = 1.0\% \]

3. **Percentage error in radius \( r \)**:
\[ \text{Percentage error in } r = \left( \frac{\Delta r}{r} \right) \times 100 = \left( \frac{0.2}{8.0} \right) \times 100 = 2.5\% \]

### Step 3: Use the formula for maximum percentage error in \( F \)
The maximum percentage error in \( F \) can be calculated using the formula:
\[ \text{Percentage error in } F = \left( 1 \times \text{Percentage error in } m \right) + \left( 2 \times \text{Percentage error in } v \right) + \left( 1 \times \text{Percentage error in } r \right) \]

Substituting the values we calculated:
\[ \text{Percentage error in } F = (1 \times 2.5\%) + (2 \times 1.0\%) + (1 \times 2.5\%) \]
\[ = 2.5\% + 2.0\% + 2.5\% = 7.0\% \]

### Conclusion
The maximum possible percentage error in the measurement of force \( F \) is:
\[ \boxed{7.0\%} \]