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Assertion: Two particles of different ma...

Assertion: Two particles of different mass, projected with same velocity at same angles. The maximum height attained by both the particle will be same.
Reason: The maximum height of projetile is independent of particle mass.

A

Statement-I is true, Statement-II is true, Statement-II is correct explanation for Statement-I

B

Statement-I is true, Statement-II is true, Statement-II is NOT a correct explanation for Statement-I

C

Statement-I is true, Statement-II is false

D

Statement-I is false, Statement-II is true.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze the assertion and reason provided: **Assertion:** Two particles of different mass, projected with the same velocity at the same angles, will attain the same maximum height. **Reason:** The maximum height of a projectile is independent of the particle's mass. ### Step-by-Step Solution: 1. **Understanding Projectile Motion:** - In projectile motion, the maximum height (H) attained by a projectile is determined by its initial velocity (u), the angle of projection (θ), and the acceleration due to gravity (g). 2. **Formula for Maximum Height:** - The formula for the maximum height (H) is given by: \[ H = \frac{u^2 \sin^2 \theta}{2g} \] - Here, \( u \) is the initial velocity, \( \theta \) is the angle of projection, and \( g \) is the acceleration due to gravity. 3. **Analyzing the Given Conditions:** - The assertion states that two particles of different masses are projected with the same initial velocity (u) and at the same angle (θ). - Since both particles are projected with the same initial velocity and angle, we can conclude that the terms \( u \) and \( \theta \) are the same for both particles. 4. **Independence from Mass:** - In the formula for maximum height, there is no term that includes mass (m). This indicates that the maximum height attained by a projectile does not depend on its mass. - Therefore, regardless of the mass of the particles, if they are projected with the same velocity and angle, they will reach the same maximum height. 5. **Conclusion:** - Since the maximum height is independent of mass, both particles will indeed reach the same maximum height when projected under the given conditions. - Thus, both the assertion and the reason are true, and the reason correctly explains the assertion. ### Final Answer: Both the assertion and reason are true, and the reason is the correct explanation for the assertion.

To solve the question, we need to analyze the assertion and reason provided: **Assertion:** Two particles of different mass, projected with the same velocity at the same angles, will attain the same maximum height. **Reason:** The maximum height of a projectile is independent of the particle's mass. ### Step-by-Step Solution: ...
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