Figure shows a cubical block of side 10 cm and relative density 1.5 suspended by a wire of cross-sectional area 10^-6m².The breaking stress of the wire is 7 x 10⁶ N/m². The block is placed in a beaker of base area 200 cm² and initially i.e. at t=0, the top surface of water and the block coincide. There is a pump at the bottom corner which ejects 2 cm³ of water per sec. If the time at which the wire will break is N x 10² sec. The value of N is_______.

Difficult

Solution

$Breaking force = Breaking stress \times area of wire$
$= 7 \times 10^{6} \times 10^{- 6} = 7 N$
$weight of block = vol \times density \times g$
$= 10^{- 3} \times (1.5 \times 10^{3}) \times 10 = 15 N$
$The up thrust when the liquid level has descended by \times cm .$
$= 100 (10 - x) \cdot 10^{- 6} \cdot 10^{3} .10 = 10 - x Newton.$
$∴ Net downward force on the block$
$= 15 - (10 - x) = 5 + x = Tension T$
$∴ The wire will break when 5 + x = 7 .$
$i.e. when x = 2 cm$
Let the level descends by 2 cm in t time then
t = 100 sec.

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