Momentum-time graph of an object moving along a straight line is as shown in figure. If (P2 – P1) < P1 and (t2 – t1) = t1 < (t3 – t2) then at which points among A, B and C the magnitude of force experienced by the object is maximum and minimum respectively.
- A, B
- A, C
- B, C
- B, A
The Correct Option is B
Solution and Explanation
Force Analysis for Different Intervals
Given Formulas:
The forces in different intervals are given by:
- \( F_A = \frac{P_1}{t_1} \)
- \( F_B = \frac{P_2 - P_1}{t_2 - t_1} \)
- \( F_C = \frac{P_2 - P_1}{t_3 - t_2} \)
Step-by-Step Solution:
1. Comparison of Forces:
- The force \( F_A \) is calculated over the smallest interval \( t_1 \), leading to the highest force value.
- The force \( F_C \) is calculated over the largest interval \( t_3 - t_2 \), leading to the lowest force value.
2. Conclusion:
- The maximum force occurs at \( A \).
- The minimum force occurs at \( C \).
Final Answer:
The correct answer is (B): A, C.
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Concepts Used:
Newtons Laws of Motion
Newton’s First Law of Motion:
Newton’s 1st law states that a body at rest or uniform motion will continue to be at rest or uniform motion until and unless a net external force acts on it.
Newton’s Second Law of Motion:
Newton’s 2nd law states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the object’s mass.
Mathematically, we express the second law of motion as follows:
Newton’s Third Law of Motion:
Newton’s 3rd law states that there is an equal and opposite reaction for every action.