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:
A. $ 5\sqrt 3 m $
B. $ 10\sqrt 3 m $
C. $ 20\sqrt 3 m $
D. $ 30\sqrt 3 m $

Answer 1

Hint: To solve this question, first we will assume the given dimensions of the hall as the final coordinate of the fly. And we will also assume the initial coordinate as the origin. Now, we can find the magnitude of its displacement.

Complete step by step solution:
The given dimensions of the hall is $ 10m \times 10m \times 10m $ .
Now, we will suppose the given dimensions as the final coordinates of fly $ (10,10,10) $ .
Then, we will assume the initial coordinates of fly $ (0,0,0) $ , starting end of room to be origin.
Thus, it undergoes a displacement of 10 along each dimension.
Now, we will find the magnitude of the displacement according to the final coordinates:
$\therefore \sqrt {{x^2} + {y^2} + {z^2}} $
$ = \sqrt {{{10}^2} + {{10}^2} + {{10}^2}} $
$ = \sqrt {100 + 100 + 100} $
$ = \sqrt {300} $
$ = 10\sqrt 3 m $
Therefore, the magnitude of its displacement is $ 10\sqrt 3 m $ .
Hence, the correct option is B. $ 10\sqrt 3 m $ .

Note:
In this question, if a fly is not starting from the one corner or if it starts from a particular point of the hall. Then the initial coordinates are not as origin. In that case, to find the magnitude of the displacement is a little bit tricky. In that case, we will assume the initial coordinates as $ ({x_1},{y_1},{z_2}) $ and the final coordinate as $ ({x_2},{y_2},{z_2}) $ .