Q.

Figure shows a cubical block of side 10 cm and relative density 1.5 suspended by a wire of cross-sectional area 106m2 . The breaking stress of the wire is 7×106N/m2 . The block is placed in a beaker of base area 200cm2 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 2cm3 of water per sec. Find the time (in sec) at which the wire will break.

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Detailed Solution

Breaking force=Breaking stress×area of wire

=7×106×106=7N

Weight of block= vol×density×g

=103×1.5×103×10=15N

The upthrust when the liquid level has descended by x cm.

=100(10x)10610310=10xN

 The wire will break when 

T=mg-B

5 + x = 7 i.e. when x = 2 cm

Let the level descends by 2 cm in t time then 

t=1sec2cm3×2cm×10cm×10cm

t = 100 sec.

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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 7×106N/m2 . The block is placed in a beaker of base area 200cm2 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 2cm3 of water per sec. Find the time (in sec) at which the wire will break.