Question

A hall has the dimensions$10mx12mx14m$. A fly starting at one corner ends up at a diagonally opposite corner. What is the magnitude of its displacement?

• A. $17m$
• B. $26m$
• C. $36m$
• D. $21m$

Answer 1

The correct option is D

$21m$

Step 1. Given Data,

The dimensions of the hall $l=10m,b=14m$ and $h=12m$.

Let the magnitude of displacement be $d.$

Step 2. The magnitude of displacement,

Since, A fly starting at one corner ends up at a diagonally opposite corner hence the displacement will be the diagonal of the hall.

The magnitude of displacement $d=$Diagonal of Hall $\left(\sqrt{l^2+b^2+h^2}\right)$

Since, we know that, the diagonal of a cube $=\sqrt{l^2+b^2+h^2}$

Therefore,

$$\begin{gathered} d=\sqrt{l^2+b^2+h^2} \\ =\sqrt{{10}^2+{14}^2+{12}^2} \end{gathered}$$

$$\begin{gathered} =\sqrt{100+196+144} \\ =\sqrt{440} \\ =2\sqrt{110} \\ =2x10.4880 \\ =20.97\simeq 21m \end{gathered}$$

Hence, option D is correct.