
Assertion: Relative velocity of A w.r.t B is greater than the velocity of either, when they are moving in opposite directions.
Reason: Relative velocity of A w.r.t B = \[\overrightarrow {{v_A}} - \overrightarrow {{v_B}} \]
A) Both assertion and reason are correct and the reason is the correct explanation for the assertion
B) Both assertion and reason are correct and the reason is not the correct explanation for the assertion
C) Assertion is correct but reason is incorrect.
D) Both assertion and reason are incorrect.
Answer
164.1k+ views
Hint:
According to the question, velocities are in the opposite direction. First, determine the velocity of A w.r.t B by applying the given condition. Then, relate the result with the assertion as well as the reason to find out the correctness of both statements. Further, choose the option which matches the valid outcome.
Complete step by step solution:
Let us assume that there are two bodies A and B respectively and the velocity of the A is $\overrightarrow {{v_A}}$ and the velocity of the B is $\overrightarrow {{v_B}}$. And the velocity of the A w.r.t the velocity of B is $\overrightarrow {{v_{AB}}}$.
Now according to the question, both the bodies A and B are moving in the opposite direction. Suppose that body B is moving in the opposite direction to body A. Therefore, the velocity of body B will be $ - \overrightarrow {{v_B}}$.
Now we know that the relative velocity of the body with respect to another body may be determined as,
$\overrightarrow{v_{12}}=\overrightarrow{v_{1}}-\overrightarrow{v_{2}}$
Therefore,
$\Rightarrow\overrightarrow{v_{AB}}=\overrightarrow{v_{A}}-\lgroup~-\overrightarrow{v_{B}}\rgroup$
$\Rightarrow\overrightarrow{v_{AB}}=\overrightarrow{v_{A}}+\overrightarrow{v_{B}}$
Now, we know that magnitude of the relative velocity is greater than the velocity of either A or B. Therefore,
$\mid\overrightarrow{v_{AB}}\mid\geqslant\mid\overrightarrow{v_{A}}+\overrightarrow{v_{B}}\mid$
Therefore, from the above relation, we can conclude that the assertion is true and the reason is incorrect.
Also, if both bodies A and B are moving in the same direction. Then, the velocity of A w.r.t B will be $\overrightarrow {{v_A}} - \overrightarrow {{v_B}}$. Thus, for the condition mentioned in the assertion, the reason is incorrect.
The correct option is C.
Note:
In this question, the first point is to keep in mind when the two bodies are moving in the opposite direction to each other, then the velocity of either A or B may be taken as negative. In other words, we can say that we should use the sign convention properly.
According to the question, velocities are in the opposite direction. First, determine the velocity of A w.r.t B by applying the given condition. Then, relate the result with the assertion as well as the reason to find out the correctness of both statements. Further, choose the option which matches the valid outcome.
Complete step by step solution:
Let us assume that there are two bodies A and B respectively and the velocity of the A is $\overrightarrow {{v_A}}$ and the velocity of the B is $\overrightarrow {{v_B}}$. And the velocity of the A w.r.t the velocity of B is $\overrightarrow {{v_{AB}}}$.
Now according to the question, both the bodies A and B are moving in the opposite direction. Suppose that body B is moving in the opposite direction to body A. Therefore, the velocity of body B will be $ - \overrightarrow {{v_B}}$.
Now we know that the relative velocity of the body with respect to another body may be determined as,
$\overrightarrow{v_{12}}=\overrightarrow{v_{1}}-\overrightarrow{v_{2}}$
Therefore,
$\Rightarrow\overrightarrow{v_{AB}}=\overrightarrow{v_{A}}-\lgroup~-\overrightarrow{v_{B}}\rgroup$
$\Rightarrow\overrightarrow{v_{AB}}=\overrightarrow{v_{A}}+\overrightarrow{v_{B}}$
Now, we know that magnitude of the relative velocity is greater than the velocity of either A or B. Therefore,
$\mid\overrightarrow{v_{AB}}\mid\geqslant\mid\overrightarrow{v_{A}}+\overrightarrow{v_{B}}\mid$
Therefore, from the above relation, we can conclude that the assertion is true and the reason is incorrect.
Also, if both bodies A and B are moving in the same direction. Then, the velocity of A w.r.t B will be $\overrightarrow {{v_A}} - \overrightarrow {{v_B}}$. Thus, for the condition mentioned in the assertion, the reason is incorrect.
The correct option is C.
Note:
In this question, the first point is to keep in mind when the two bodies are moving in the opposite direction to each other, then the velocity of either A or B may be taken as negative. In other words, we can say that we should use the sign convention properly.
Recently Updated Pages
Uniform Acceleration - Definition, Equation, Examples, and FAQs

JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Main 2025 Session 2: Exam Date, Admit Card, Syllabus, & More

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

Trending doubts
Atomic Structure - Electrons, Protons, Neutrons and Atomic Models

Learn About Angle Of Deviation In Prism: JEE Main Physics 2025

Charging and Discharging of Capacitor

A body of mass 3Kg moving with a velocity of 4ms towards class 11 physics JEE_Main

Class 11 JEE Main Physics Mock Test 2025

JEE Main Chemistry Question Paper with Answer Keys and Solutions

Other Pages
JEE Advanced 2025 Notes

Total MBBS Seats in India 2025: Government College Seat Matrix

NEET Total Marks 2025: Important Information and Key Updates

Neet Cut Off 2025 for MBBS in Tamilnadu: AIQ & State Quota Analysis

Karnataka NEET Cut off 2025 - Category Wise Cut Off Marks

NEET Marks vs Rank 2024|How to Calculate?
