Question

Consider two particles $P$ and $Q$. Particle $P$ moves from $A$ to $B$ and particle $Q$ moves from $C$ to $D$. If the displacement of particle $P$ and $Q$ be $x$, $y$ respectively. Then:

• A. $x=y$
• B. $x<y$
• C. $x>y$
• D. $x\ge y$

Answer 1

The correct option is C $x>y$

when particle $P$ moves from $A$ to $B$, from the given figure we can see that its displacement is $AB$.
From right angled triangle, $\Delta OAB$:
$AB=\sqrt{(OA{)}^2+(OB{)}^2}$
$\Rightarrow AB=\sqrt{(2{)}^2+(5{)}^2}=\sqrt{29}\text{m}$
$\Rightarrow x=AB=\sqrt{29}\text{m}$

when particle $Q$ moves from $C$ to $D$, from the given figure we can see that its displacement is $CD$.
From right angled triangle, $\Delta ODC$:
$CD=\sqrt{(OC{)}^2+(OD{)}^2}$
$\Rightarrow CD=\sqrt{(3{)}^2+(4{)}^2}=\sqrt{25}=5\text{m}$
$\Rightarrow y=CD=5\text{m}$
Hence $x>y$