Question

Assertion: The dimensional formula for relative velocity is the same as that of the change in velocity.
Reason: Relative velocity of P w.r.t. Q is the ratio of velocity of P and that of Q.
(A) Both assertion and reason are true and the reason is the correct explanation of assertion.
(B) Both assertion and reason are true but the reason is not the correct explanation of assertion.
(C) Assertion is true but the reason is false.
(D)Both the assertion and reason are false.
(E) Reason is true but the assertion is false.

Answer 1

Hint To solve the question, you must first check whether assertion and reason are true or not, once you have figured it out, you need to check whether the reason is the correct reason for the assertion or not, if the reason is true. Then, marks the option that you deem the most suitable.

Complete step by step answer:
To solve the question, we first need to have the basic understanding of relative velocity and the fact that it may not be what its name gives away about it.
Let us assume a particle P is moving with a velocity of magnitude ${v_p}$ in a certain direction.
Let us also assume that another particle Q is also moving along the same direction with a magnitude of ${v_q}$. Now, we can give the relative velocity of P with respect to Q as following:
${v_r} = {v_p} - {v_q}$
As we can see, the relative velocity is just the difference of two velocities, it will have the same dimensional formula as the dimensional formula of change in velocity which in turn will also have the same dimensional formula as that of velocity.
The dimensional formula of all these terms will be given as: $\left[ {L{T^{ - 1}}} \right]$
Now, we have developed the fact that the assertion is true.
Let us check the credibility of the statement for the reason.
Reason stats that: “Relative velocity of P w.r.t. Q is the ratio of velocity of P and that of Q.”
We have already seen that relative velocity is not the ratio of velocities of P and Q, rather it is the difference of velocities of particles P and Q. Hence, we can confidently say that the reason is not only the wrong reason, but false itself.

Now if we check the options, we can clearly see that the answer is nothing but option (C) as it states that the assertion is true but the reason is false, which is actually the case here.

Note Since the term relative is used when there is a ratio of two quantities, many students get confused and assume that the same case may be with the relative velocity that it is the ratio of two velocities, which is completely wrong.