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Consider the following two statements: Statement 1: If two stones are thrown from the same point on the ground at the same instant but with different initial velocities, they cannot meet each other in mid-air. (Ignore air resistance.) Statement 2: When two particles start from the same position and their relative acceleration remains zero at all times, the separation between them either stays unchanged or keeps increasing with time. Which of the following is correct? (a) Statement 1 is false, Statement 2 is true. (b) Statement 1 is true, Statement 2 is true, and Statement 2 correctly explains Statement 1. (c) Statement 1 is true, Statement 2 is true, but Statement 2 does not correctly explain Statement 1. (d) Statement 1 is true, Statement 2 is false.

1. (a) Statement 1 is false, Statement 2 is true.
2. (b) Statement 1 is true, Statement 2 is true, and Statement 2 correctly explains Statement 1.
3. (c) Statement 1 is true, Statement 2 is true, but Statement 2 does not correctly explain Statement 1.
4. (d) Statement 1 is true, Statement 2 is false.

Correct answer: (b) Statement 1 is true, Statement 2 is true, and Statement 2 correctly explains Statement 1.

Solution

Statement 1 is true because two stones with different velocities will follow different trajectories and cannot meet in mid-air. Statement 2 is also true as it describes that if two particles have zero relative acceleration, their distance will either remain constant or increase, which aligns with the idea that differing velocities prevent them from converging.

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