Question

Ten boxes each of mass $5\text{kg}$ are stacked on top of each other and are being carried upwards in an elevator. Each box can sustain a maximum load of $250\text{N}$ at its top surface. If the acceleration of the lift is $3\text{m}/s^2$, then, how many boxes will get damaged at their top surface?
Take $g=10{\text{m/s}}^2$ .

• A. No boxes get damaged
• B. $6$ boxes get damaged
• C. $5$ boxes get damaged
• D. $7$ boxes get damaged

Answer 1

The correct option is B $6$ boxes get damaged

Every box except topmost one experiences a normal force on its top surface, due to the box on top of it

$\Rightarrow$Normal force on top surface of n${}^{th}$ block is
$F=\left[\right(n-1\left)m\right(g+a\left)\right]N$
(where, $n$ is $n^{th}$ box from top)

To avoid damaging of boxes:

$F\le F_{\text{max}}$
Or,
$F\le 250\text{N}$

$(n-1)m(g+a)\le 250\Rightarrow (n-1)\times 5\times (10+3)\le 250\Rightarrow 65n-65\le 250\Rightarrow n\le 4.84$
$\therefore$ for the value of $n$ $\le 4.84$, the boxes will not get damaged.

So, undamaged boxes$=4$
$\therefore$ Damaged boxes$=(10-4)=6$