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(A) : Stationary bomb explodes into two ...

(A) : Stationary bomb explodes into two fragments. They move with different velocities in oppsite directions.
(R ) : Explosion does not violate the low of conservation of linear momentum.

A

Both (A) and (R ) are true and (R ) is the correct explanation of (A)

B

Both (A) and (R ) are true and (R ) is not the correct explanation of (A)

C

(A) is true but (R ) is false

D

Both (A) and (R ) are false

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze the assertion and reason provided regarding the explosion of a stationary bomb and the conservation of linear momentum. ### Step-by-Step Solution: 1. **Understanding the System**: - We consider the bomb as a system that is initially stationary. This means that the total momentum of the system before the explosion is zero. 2. **Explosion and Internal Forces**: - When the bomb explodes, it breaks into two fragments. The explosion is caused by internal forces acting within the bomb. Since these forces are internal, they do not affect the total momentum of the system. 3. **Conservation of Linear Momentum**: - According to the law of conservation of linear momentum, if no external forces act on a system, the total momentum of the system remains constant. In this case, since the bomb is stationary before the explosion, the initial momentum is zero. 4. **Analyzing the Fragments**: - Let’s denote the masses of the two fragments as \( m_1 \) and \( m_2 \), and their velocities after the explosion as \( v_1 \) and \( v_2 \) respectively. - After the explosion, the fragments move in opposite directions. Therefore, we can express the final momentum of the system as: \[ m_1 v_1 + m_2 v_2 = 0 \] - This implies that \( m_1 v_1 = -m_2 v_2 \). The negative sign indicates that the velocities are in opposite directions. 5. **Conclusion**: - Since the total momentum before the explosion (initial momentum) is zero and the total momentum after the explosion (final momentum) is also zero, the law of conservation of linear momentum is upheld. - Therefore, both the assertion and the reason are true, and the reason correctly explains the assertion. ### Final Answer: - Both the assertion (A) and the reason (R) are true, and R is the correct explanation for A.
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