A ball weighing `10g` hits a hard surface vertically with a speed of `5m//s` and rebounds with the same speed The ball remains in contact with the surface speed The ball remains in contact with the surface for `0.01s` The average force exerted by the surface on the ball is .

Options

A. `100N`
B. `10N`
C. `1N`
D. `0.1N`

Explanation

To solve the problem of finding the average force exerted by the surface on the ball, we can follow these steps:

### Step 1: Understand the Problem
The ball weighs 10 grams and hits the surface with a speed of 5 m/s, then rebounds with the same speed. The time of contact with the surface is 0.01 seconds. We need to calculate the average force exerted by the surface on the ball.

### Step 2: Convert Mass to Kilograms
Since the standard unit of mass in physics is kilograms, we need to convert the mass of the ball from grams to kilograms:
\[ \text{Mass (m)} = 10 \text{ g} = 0.01 \text{ kg} \]

### Step 3: Calculate Initial and Final Velocities
- The initial velocity (when hitting the surface) is:
\[ V_i = -5 \text{ m/s} \quad (\text{downward direction is negative}) \]
- The final velocity (when rebounding) is:
\[ V_f = 5 \text{ m/s} \quad (\text{upward direction is positive}) \]

### Step 4: Calculate Change in Momentum
The change in momentum (\(\Delta P\)) can be calculated using the formula:
\[ \Delta P = m(V_f - V_i) \]
Substituting the values:
\[ \Delta P = 0.01 \text{ kg} \times (5 \text{ m/s} - (-5 \text{ m/s})) \]
\[ \Delta P = 0.01 \text{ kg} \times (5 + 5) \text{ m/s} = 0.01 \text{ kg} \times 10 \text{ m/s} = 0.1 \text{ kg m/s} \]

### Step 5: Calculate Average Force
The average force (\(F\)) can be calculated using the formula:
\[ F = \frac{\Delta P}{\Delta t} \]
Where \(\Delta t\) is the time of contact (0.01 s):
\[ F = \frac{0.1 \text{ kg m/s}}{0.01 \text{ s}} = 10 \text{ N} \]

### Conclusion
The average force exerted by the surface on the ball is:
\[ \boxed{10 \text{ N}} \]