Question

Velocity of five particles $A,B,C,D$ and $E$ varies with time $t$ as, $\overrightarrow{V_A}=(8t\hat{i}+6\hat{j})m{s}^{-1},\overrightarrow{V_B}=(4\hat{i}+3\hat{j})m{s}^{-1},$
$\overrightarrow{V_C}=(6\hat{i}-4t\hat{j})m{s}^{-1},\overrightarrow{V_D}=(-3t\hat{i}+5\hat{j})m{s}^{-1}$ and $\overrightarrow{V_E}=(2\hat{i}+5t\hat{j})m{s}^{-1}.$
Match the pseudo force as observed and specified in column $I$ to the respective direction given in column $II$.
$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \left(A\right)\text{On A as observed by B}& \left(p\right)\text{Along positive X direction}\\ \left(B\right)\text{On B as observed by C}& \left(q\right)\text{Along negative X direction}\\ \left(C\right)\text{On C as observed by D}& \left(r\right)\text{Along positive Y direction}\\ \left(D\right)\text{on D as observed by E}& \left(s\right)\text{Along negative Y direction}\\ \left(E\right)\text{On E as observed by A}& \left(t\right)\text{zero}\end{array}$

• A. $\left(A\right)\to \left(p\right),\left(B\right)\to \left(r\right),\left(C\right)\to \left(p\right),\left(D\right)\to \left(s\right),\left(E\right)\to \left(q\right)$
• B. $\left(A\right)\to \left(t\right),\left(B\right)\to \left(r\right),\left(C\right)\to \left(p\right),\left(D\right)\to \left(s\right),\left(E\right)\to \left(q\right)$
• C. $\left(A\right)\to \left(t\right),\left(B\right)\to \left(r\right),\left(C\right)\to \left(s\right),\left(D\right)\to \left(s\right),\left(E\right)\to \left(q\right)$
• D. $\left(A\right)\to \left(p\right),\left(B\right)\to \left(r\right),\left(C\right)\to \left(q\right),\left(D\right)\to \left(s\right),\left(E\right)\to \left(q\right)$

Answer 1

The correct option is B $\left(A\right)\to \left(t\right),\left(B\right)\to \left(r\right),\left(C\right)\to \left(p\right),\left(D\right)\to \left(s\right),\left(E\right)\to \left(q\right)$

Pseudo force comes to play, when the frame of reference (from where the phenomenon is being observed) is accelerating.
For the observation frames A, B, C, D and E, respectively the accelerations are:
$\overrightarrow{a_A}=8\hat{i},\overrightarrow{a_B}=0,\overrightarrow{a_c}=-4\hat{j},\overrightarrow{a_D}=-3\hat{i}\overrightarrow{a_E}=5\hat{j}$

The pseudo force is then directed opposite to the acceleration of the observation frame(frame of reference).
Hence, the pseudo force on A as observed by B is zero.$\because \overrightarrow{a_B}=0$
The pseudo force on B as observed by C is along +Y direction $\because \overrightarrow{a_c}=-4\hat{j}$
The pseudo force on C as observed by D is along +X direction $\because \overrightarrow{a_D}=-3\hat{i}$
The pseudo force on D as observed by E is along -Y direction $\because \overrightarrow{a_E}=5\hat{j}$
The pseudo force on E as observed by A is along -X direction $\because \overrightarrow{a_A}=8\hat{i}$