Question

Velocity of three particles A, B and C varies with time t as, ${\overrightarrow{v}}_A=(2t\hat{i}+6\hat{j})m/s,{\overrightarrow{v}}_B=(3\hat{i}+4\hat{j})m/s$ and ${\overrightarrow{v}}_C=(6\hat{i}-4t\hat{j})$. Regarding the pseudo force match the following:

Column I	Column II
(a) on A as observed by B	(p) along positive x-direction
(b) on B as observed by C	(q) along negative x-direction
(c) on A as observed by C	(r) along positive y-direction
(d) on C as observed by A	(s) along negative y-direction
	(t) zero

• A. (a-p), (b-q), (c-r), (d-s)
• B. (a-t), (b-r), (c-r), (d-q)
• C. (a-t), (b-s), (c-r), (d-p)
• D. none of these

Answer 1

The correct option is B (a-t), (b-r), (c-r), (d-q)

A force having acceleration a will make

all the bodies in this force, feel a pseudo

force $-$ma; m$-$ mass of that body

$\overrightarrow{V_A}=2t\hat{i}+6\hat{j}\Rightarrow \overrightarrow{a_n}=\frac{d\overrightarrow{V_A}}{dt}=2\hat{i}+0$

$\overrightarrow{V_B}=3\hat{i}+4\hat{j}\Rightarrow \overrightarrow{a_B}=0$

$\overrightarrow{V_C}=6\hat{i}-4t\hat{j}\Rightarrow \overrightarrow{a_C}=-4\hat{i}$

$\bullet$ B is an inertial force so pseudo force$=0$

$\Rightarrow a-t$

$\bullet$ C has -ve i.e awrl $-\hat{i}$ so pseudo

force on all force shed be along $+\hat{i}$

So $b-rc-r$

$\bullet$ A is Non-inertial & haring accelerate

awns +ve $\hat{i}$ so pseudo force

on all bodys (force) w.r.t A

will be allwns -ve $\hat{i}$

So $d-2$