Figure shows a cubical block of side 10 cm and relative density 1.5 suspended by a wire of cross sectional area `10^(-6) m^(2)`. The breaking stress of the wire is `7 xx 10^(6) N//m^(2)`. The block is placed in a beaker of base area `200 cm^(2)` and initially i.e. at t = 0, the top surface of water & the block coincide. There is a pump at the bottom corner which ejects `2 cm^(3)` of water per sec. Find the time at which the wire will break.

Answer

5

Explanation

Breaking force `=` Breaking stress `xx` area of wire
`= 7 xx 10^(6) xx 10^(-6) = 7N`
weight of block `= vol xx density xx g`
`10^(-3) xx (1.5 xx 10^(3)) xx 10`
`= 15 N`.
The upthrust when the liquid level has decended by `x cm`.
`= 100 (10 - x). 10^(-6). 10^(3). 10`
`= 10 - x` Newton.
`:.` Net downward force on the block `= 15 - (10 - x) = 5 + x = "Tansion" T`
`:.` The wire will break when `5 + x = 7`.
i.e. when `x = 2cm`
Let the level decends by `2 cm` in `t` time
then `2t = (200 - 100).2`
`t = 100 sec`. ........Ans.
`20x = 10 :. x = 5`