GATE mechanical puzzles

Replies

• 

  Reya

  @ishu :29.4 ?
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  ISHAN TOPRE

  Pravee, what volume have you considered? It it 1 m3?
  Please post your solution along with units 😀
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  ISHAN TOPRE

  2. We will discuss first question, meanwhile here is next.
  
  In a container there is a mercury ( density=13600 Kg/m3) and on top of it is a layer of water (density=1000 Kg/m3) A body is floating on the interface of the two liquids so that it is 30% submerged in mercury and 70% in water. What is the density of that body?
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  ISHAN TOPRE

  I think it is wrong Praveena. What is the volume of body you assumed? 1m3? I forgot to mention it Sorry.
  
  P.S: I think the question may come in CAT.
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  Reya

  704.08 😀
  
  Let Volume of the body=v m^3
  
  Specific gravity of the mercury=13.6
  
  Vol of the body drowned in Hg= 30%=30/100=0.3v
  
  vol of the body drowned in H2O=70%=70/100=0.7v
  
  weight of the body= specific gravity*gravitational force*volume
  
  weight of mercury displaced by body= 13.6*9.81*0.3 v
  
  weight of water displaced by body= 1000*9.81*0.7 v
  
  weight of body=weight of mercury displaced by body+weight of water displaced by body
  
  p(row)*g*v=13.6*9.81*0.3 v+1000*9.81*0.7 v
  
  p(row)=704.08 kg/m^3
• 

  ISHAN TOPRE

  So the answer to second problem is correct. 😀
  
  The solution to first problem is force= weight of body-buoyancy force= 3000*9.81*1-1000*9.81*1=19620N
• 

  Reya

  Buoyancy means weight of displaced body. Just now i came to know that 😔
  
  PS: Sorry for spamming!
• 

  ISHAN TOPRE

  praveena211

  Buoyancy means weight of displaced body.

  Eureka! Eureka! even Archimedes would have spammed. 😁
  
  OK Here is another question.
  
  3. If you have a rectangular tank (open from top) and it is completely filled with water. The dimensions of tank are 8m length, 3m wide and 2 m deep. If you move it with a constant acceleration of 3 m/s2 in the direction of length, how much water will be spilled from tank? 😀
  
  
  hint: Try to find out the volume of water in triangle which equals the volume of displaced water.
  Find out area of triangle and multiply it by width.
• 

  ISHAN TOPRE

  Now shifting the point of spilling water to the center. we can calculate the angle as tan(angle)= adj side/opp side.
  
  
  
  tan(angle)=a/g= 3/9.81= 17.004 degrees
  
  tan (angle)=h/4. where 4 is half of the container length (8m)
  
  Now we know tan (angle) we can calculate the depth h which comes out to be 1.223m.
  
  Now volume of water spilled=1.223X4X3=14.679m3 👍