GATE mechanical puzzles

I am starting this thread with a hope of studying some technical puzzles. I am starting with a simple question, and I will start increasing difficulty level as we advance. Feel free to post answers.

My first question:

A body of specific gravity 3.0 is immersed in water. What is the minimum force required to pull it out?
Consider volume of body as 1 m3

P.S: Spamming is strictly discouraged, ONLY technical discussion expected.


  • Reya
    @ishu :29.4 ?
    Pravee, what volume have you considered? It it 1 m3?
    Please post your solution along with units ๐Ÿ˜€
    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?
    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.
  • Reya
    704.08 ๐Ÿ˜€

    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
    So the answer to second problem is correct. ๐Ÿ˜€

    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 ๐Ÿ˜”

    PS: Sorry for spamming!
    Buoyancy means weight of displaced body.
    Eureka! Eureka! even Archimedes would have spammed. ๐Ÿ˜

    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? ๐Ÿ˜€

    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.
    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 ๐Ÿ‘

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