A wooden block of mass 8 kg is tied to a string attached to the bottom of the tank. In equilibrium , the block is completely immersed in water. If relative density of wood is 0.8 and g = 10 m / s2 then what is the value of tension in the string.

Asked by Paresh | 18th Nov, 2015, 06:26: PM

Expert Answer:

Given:
 Mass of the wooden block, m= 8kg
 Relative density of wood = 0.8
We know that: 
begin mathsize 14px style fraction numerator Density space of space wood over denominator Density space of space water end fraction equals Relative space density space of space wood fraction numerator Density space of space wood over denominator Density space of space water end fraction equals 0.8 Density space of space wood space equals space 0.8 space cross times Density space of space water Density space of space wood space equals space 0.8 space cross times 1000 space Kg divided by straight m cubed end style
 
The upthrust experienced by the wooden block upward will be balanced by the weight of the wooden block acting downwards + the tension on the string
i.e. Upthrust = Weight + Tension
Therefore the tension on the string = Upthrust - Weight
The upthrust experienced by the wooden block = Volume of water displaced by the block × Density of water × g
 
begin mathsize 14px style Volume space of space water space displaced space by space the space block space equals fraction numerator Mass space of space the space wood space block over denominator Density space of space wood space end fraction straight V space equals fraction numerator 8 over denominator 0.8 cross times 1000 end fraction end style
 
begin mathsize 14px style Upthrust space equals space fraction numerator 8 over denominator 0.8 cross times 1000 end fraction cross times space 1000 space cross times space 10 space space space space space space space space space space space space space space space equals 100 space straight N end style
 
Tension on the string = Upthrust - Weight
                              = 100 N - (8 ×10) N
                              = 20 N
Therefore Tension on the sring = 20N

Answered by Yashvanti Jain | 18th Nov, 2015, 06:35: PM