Two bodies x and y of weight 600 N and 1000 N are dropped simultaneously from the same height above the earth's surface from same place. Their accelerations will be

Options

A. `a_(x)gt a_(y)`
B. `a_(y)gt z_(x)`
C. `a_(x)=a_(y)`
D. Can't be predicted

Answer

To solve the problem of two bodies x and y with weights of 600 N and 1000 N dropped from the same height, we need to determine their accelerations.

### Step-by-Step Solution:

1. **Understanding Weight and Mass**:
- The weight (W) of an object is related to its mass (m) and the acceleration due to gravity (g) by the equation:
\[ W = m \cdot g \]
- For body x, with a weight of 600 N:
\[ W_x = m_x \cdot g \implies 600 = m_x \cdot g \quad (1) \]
- For body y, with a weight of 1000 N:
\[ W_y = m_y \cdot g \implies 1000 = m_y \cdot g \quad (2) \]

2. **Calculating Masses**:
- Rearranging equations (1) and (2) gives us the masses:
\[ m_x = \frac{600}{g} \quad (3) \]
\[ m_y = \frac{1000}{g} \quad (4) \]

3. **Acceleration Calculation**:
- The acceleration (a) of an object in free fall is given by the formula:
\[ a = \frac{W}{m} \]
- For body x:
\[ a_x = \frac{W_x}{m_x} = \frac{600}{m_x} = \frac{600}{\frac{600}{g}} = g \quad (5) \]
- For body y:
\[ a_y = \frac{W_y}{m_y} = \frac{1000}{m_y} = \frac{1000}{\frac{1000}{g}} = g \quad (6) \]

4. **Conclusion**:
- From equations (5) and (6), we see that both bodies experience the same acceleration due to gravity:
\[ a_x = a_y = g \]

Thus, the accelerations of both bodies x and y are equal to the acceleration due to gravity (g).

### Final Answer:
The accelerations of both bodies x and y are equal to \( g \) (approximately \( 9.81 \, \text{m/s}^2 \)).

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