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A box is put on a scale which is adjusted to read zero, when the box is empty. A stream of pebbles is then poured into the box from a height h above its bottom at a rate of n pebbles. Each pebble has a mass m. If the pebbles collide with the box such that they immediately come to rest after collision, the scale reading at time t after the pebbles begin to fill the box is

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$mn {(2 gh) + gt}$

$\frac{{\sqrt{(2 gh) + gt}}}{mn}$

${\sqrt{(2 gh) + gt}}$

$mn {\sqrt{(2 g h)} + g t}$

answer is A.

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Detailed Solution

Scale reading = weight of pebbles in time 't' +
rate of change of momentum at time 't'
$nmgt + m \sqrt{2 gh} n = mn (\sqrt{2 gh} + gt)$

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