A bowling machine projects a ball of mass 0.15kg in upward direction. If ball displaced along bowling machine 0.2 m and released. after released from bowling machine ball attain 20 m height then find force exerted by bowling machine on ball

Options

A. 145.5 N
B. 165.5 N
C. 175.5 N
D. 151.5 N

Answer

To solve the problem, we need to determine the force exerted by the bowling machine on the ball. We will use the work-energy principle, which states that the work done on an object is equal to the change in its energy.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Mass of the ball, \( m = 0.15 \, \text{kg} \)
- Displacement in the bowling machine, \( d = 0.2 \, \text{m} \)
- Maximum height attained by the ball, \( h = 20 \, \text{m} \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \) (approximate value)

2. **Calculate the Potential Energy at Maximum Height:**
The potential energy (PE) at the maximum height can be calculated using the formula:
\[ PE = mgh \]
Substituting the values:
\[ PE = 0.15 \, \text{kg} \times 10 \, \text{m/s}^2 \times 20 \, \text{m} = 30 \, \text{J} \]

3. **Work Done by the Bowling Machine:**
The work done (W) by the bowling machine on the ball is equal to the force (F) exerted by the machine multiplied by the displacement (d):
\[ W = F \cdot d \]
Since all the work done by the bowling machine is converted into potential energy, we can set:
\[ W = PE \]
Therefore,
\[ F \cdot d = PE \]

4. **Substituting the Values:**
Rearranging the equation to find the force:
\[ F = \frac{PE}{d} \]
Substituting the known values:
\[ F = \frac{30 \, \text{J}}{0.2 \, \text{m}} = 150 \, \text{N} \]

5. **Final Answer:**
The force exerted by the bowling machine on the ball is:
\[ F = 150 \, \text{N} \]