On a planet X a man throws a 500 gm mass with a respect of 20 m/s and catches it as it comes down 20 second later. The weight of the mass is

Options

A. 1 newton
B. `10^(4)` newton
C. 10 newton
D. none of the above

Explanation

To solve the problem, we need to determine the weight of a 500 gm mass thrown on planet X with an initial velocity of 20 m/s and caught after 20 seconds.

### Step-by-Step Solution:

1. **Convert the mass from grams to kilograms**:
\[ \text{Mass} = 500 \text{ gm} = \frac{500}{1000} \text{ kg} = 0.5 \text{ kg} \]

**Hint**: Remember to convert grams to kilograms since the SI unit of mass is kilograms.

2. **Determine the total time of flight**:
The total time for the motion is given as 20 seconds. Since the object is thrown up and then comes down, the time taken to reach the maximum height is half of the total time.
\[ \text{Time to reach maximum height} = \frac{20 \text{ s}}{2} = 10 \text{ s} \]

**Hint**: The time to go up is equal to the time to come down in projectile motion.

3. **Use the first equation of motion**:
The first equation of motion relates initial velocity (u), final velocity (v), acceleration (a), and time (t):
\[ v = u + at \]
At the maximum height, the final velocity (v) is 0 m/s. The initial velocity (u) is 20 m/s, and the time (t) is 10 s. We can rearrange the equation to find acceleration (a):
\[ 0 = 20 + a(10) \]
\[ a(10) = -20 \implies a = -\frac{20}{10} = -2 \text{ m/s}^2 \]

**Hint**: The acceleration is negative because it is acting in the opposite direction to the initial velocity (gravity).

4. **Calculate the weight of the mass**:
The weight (W) of an object is given by the formula:
\[ W = m \cdot g \]
where \( g \) is the acceleration due to gravity. Here, we found \( a = -2 \text{ m/s}^2 \), which we can take as \( g \) for our calculations:
\[ W = 0.5 \text{ kg} \cdot 2 \text{ m/s}^2 = 1 \text{ N} \]

**Hint**: Weight is a force and is calculated by multiplying mass by the acceleration due to gravity.

5. **Conclusion**:
The weight of the mass is **1 Newton**.

### Final Answer:
The weight of the mass is **1 Newton**.