# 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.

## Replies

• Reya
@ishu :29.4 ?
• ISHAN TOPRE
Pravee, what volume have you considered? It it 1 m3?
• 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?
• 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.
• 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 👍

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