A body thrown up with a velocity reaches a maximum height of 50 m. Another body with double the mass thrown up with double the initial velocity will reach the maximum height of

Options

A. 100 m
B. 200 m
C. 400 m
D. 50 m

Answer

To solve the problem, we need to determine the maximum height reached by a second body that is thrown upwards with double the mass and double the initial velocity of the first body, which reaches a maximum height of 50 meters.

### Step-by-Step Solution:

1. **Understanding the First Body's Motion:**
- The first body is thrown upwards with an initial velocity \( u \) and reaches a maximum height \( h_a = 50 \, \text{m} \).
- The formula for maximum height \( h \) in terms of initial velocity \( u \) and acceleration due to gravity \( g \) is:
\[ h = \frac{u^2}{2g} \]

2. **Finding Initial Velocity of the First Body:**
- Rearranging the formula for the first body, we have:
\[ u^2 = 2gh_a \]
- Substituting \( h_a = 50 \, \text{m} \) and taking \( g = 10 \, \text{m/s}^2 \):
\[ u^2 = 2 \times 10 \times 50 = 1000 \]

3. **Understanding the Second Body's Motion:**
- The second body has double the mass (2m) and is thrown upwards with double the initial velocity (2u).
- We need to find the maximum height \( h_b \) for the second body.

4. **Using the Maximum Height Formula for the Second Body:**
- The maximum height for the second body can be calculated using the same formula:
\[ h_b = \frac{(2u)^2}{2g} \]
- Expanding this:
\[ h_b = \frac{4u^2}{2g} = \frac{2u^2}{g} \]

5. **Substituting for \( u^2 \):**
- We already found \( u^2 = 1000 \):
\[ h_b = \frac{2 \times 1000}{10} = \frac{2000}{10} = 200 \, \text{m} \]

6. **Conclusion:**
- The maximum height reached by the second body is \( h_b = 200 \, \text{m} \).

### Final Answer:
The second body will reach a maximum height of **200 meters**.