Question

A hall has the dimensions $10m\times 10m\times 10m.$ A fly starting at one corner ends up at a diagonally opposite corner. The magnitude of its displacement is nearly

• A. $5\sqrt{3}m$
• B. $10\sqrt{3}m$
• C. $20\sqrt{3}m$
• D. $30\sqrt{3}m$

Answer 1

The correct option is B $10\sqrt{3}m$

Let the dimensions of the room is depicted in the figure shown below.

Lets assume that the fly starts from corner A and reaches at corner B (which is diagonally opposite)

So, the length of the diagonal $AC$ of the bottom face
$\therefore (AC{)}^2=(AD{)}^2+(DC{)}^2$
$\Rightarrow AC=\sqrt{{10}^2+{10}^2}=10\sqrt{2}m$
Now, the length of the diagonal of the hall is given by
$\therefore (AB{)}^2=(AC{)}^2+(CB{)}^2$
$⟹AB=\sqrt{(10\sqrt{2}{)}^2+{10}^2}=10\sqrt{3}m$
Thus, the magnitude of displacement of the fly is $10\sqrt{3}m$