Question

A hall has the dimensions$10mx14mx12m$. 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 are

$$\begin{gathered} l=10m, \\ b=14m, \\ h=12m \end{gathered}$$

Step 2. Finding the magnitude of displacement

Diagonal of the hall $=\sqrt{l^2+b^2+h^2}$

Since the diagonal of the hall is the shortest distance

Therefore, the magnitude of displacement, $\begin{array}{l}d=\sqrt{{10}^2+{14}^2+{12}^2}\end{array}$

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

Hence, option $\left(D\right)$ is correct.