Two balls of different masses are thrown vertically upwards with the same speed . They pass through the point of projection in their downward motion with the same speed ( Neglect air resistance ).

Explanation

To solve the problem, we need to analyze the motion of two balls of different masses thrown vertically upwards with the same initial speed and determine if they pass through the point of projection during their downward motion with the same speed.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Two balls are thrown vertically upwards.
- Both balls have different masses.
- Both balls are thrown with the same initial speed.
- We need to analyze their motion as they return to the point of projection.

2. **Understand the Motion of the Balls:**
- When an object is thrown vertically upwards, it will rise until it reaches its maximum height, where its velocity becomes zero.
- After reaching the maximum height, the object will fall back down under the influence of gravity.

3. **Apply the Equations of Motion:**
- The equations of motion for uniformly accelerated motion (under gravity) are independent of mass. The key equation we can use is:
\[ v^2 = u^2 + 2as \]
where:
- \( v \) is the final velocity,
- \( u \) is the initial velocity,
- \( a \) is the acceleration (which is \(-g\) for upward motion),
- \( s \) is the displacement.

4. **Analyze the Upward Motion:**
- Both balls are thrown upwards with the same initial speed \( u \).
- They will rise until their velocity becomes zero at the maximum height. The time taken to reach the maximum height and the height reached will depend on the initial speed and acceleration due to gravity, but not on mass.

5. **Analyze the Downward Motion:**
- As the balls fall back down, they will pass through the point of projection (the starting point) with the same speed they were thrown upwards.
- Since both balls were thrown with the same initial speed and are subject to the same gravitational acceleration, they will return to the point of projection with the same speed.

6. **Conclusion:**
- Since the equations of motion do not depend on mass, both balls will indeed pass through the point of projection during their downward motion with the same speed.
- Therefore, the statement is **true**.

### Final Answer:
The statement is true; both balls will pass through the point of projection in their downward motion with the same speed.

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