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 $$is_______$$.

Question

Infinity Learn · Accepted Answer

Breaking force $$=$$ Breaking stress × area of wire $$=7$$×$$106$$×$$10$$−$$6=7N$$ weight of block $$=vol$$× density ×$$g=10$$−$$3$$×$$1.5$$×$$103$$×$$10=15N$$ The up thrust when the liquid level has descended by ×cm . $$=100(10$$−$$x)$$⋅$$10$$−$$6$$⋅$$103.10=10$$−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 $$x=2cmLet$$ the level descends by $$2$$ cm in t time thent $$=$$ $$100$$ $$sec$$.

Best Courses for You

Detailed Solution

courses

Get Expert Academic Guidance – Connect with a Counselor Today!

best study material, now at your finger tips!

download the app

Download the App