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.

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  • Reya
    Reya

    @reya-SMihdC • Jul 26, 2011

    @ishu :29.4 ?

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  • ISHAN TOPRE
    ISHAN TOPRE

    @ishan-nohePN • Jul 26, 2011

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

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  • ISHAN TOPRE
    ISHAN TOPRE

    @ishan-nohePN • Jul 26, 2011

    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
    ISHAN TOPRE

    @ishan-nohePN • Jul 26, 2011

    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
    Reya

    @reya-SMihdC • Jul 26, 2011

    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

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  • ISHAN TOPRE
    ISHAN TOPRE

    @ishan-nohePN • Jul 26, 2011

    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

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  • Reya
    Reya

    @reya-SMihdC • Jul 26, 2011

    Buoyancy means weight of displaced body. Just now i came to know that 😔

    PS: Sorry for spamming!

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  • ISHAN TOPRE
    ISHAN TOPRE

    @ishan-nohePN • Jul 27, 2011

    praveena211Buoyancy 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? 😀

    [​IMG]
    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.

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  • ISHAN TOPRE
    ISHAN TOPRE

    @ishan-nohePN • Aug 3, 2011

    Now shifting the point of spilling water to the center. we can calculate the angle as tan(angle)= adj side/opp side.

    [​IMG]

    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 👍

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