# Question on Archimedes principle.

1. Dec 16, 2011

### vkash

1. The problem statement, all variables and given/known data

A solid sphere of mass m=2 kilogram and specific gravity s=0.5 is held stationary to a tank as shown in figure. The tank is accelerating upward with a=2ms-2. calculate the tension in the string? If suddenly string break then the acceleration of the ball in frame of tank.
2. Relevant equations

Archimedes principle

3. The attempt at a solution
see in attachment.
for second question. My answer is
net force =B-mg=20 so acceleration in frame of ground is 10. In frame it should 10-2=8.

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Last edited: Dec 16, 2011
2. Dec 16, 2011

### ehild

Hi Vkash,

ehild

3. Dec 16, 2011

### vkash

I have tried to answer these questions. Where am i wrong.

4. Dec 16, 2011

### ehild

The problem is easiest to solve if you use the accelerating frame of reference, fixed to the tank. Have you learnt about accelerating frames of reference? You feel heavier in a lift which accelerates upward as if the gravitational acceleration g would be bigger. And you feel lighter in a frame of reference accelerating downward. In a falling lift you are weightless.

Buoyant force arises because of the weight of the liquid. In a falling tank, there would be no buoyant force. You could immerse any object into the liquid, it would stay at the same place.
This tank accelerates upward with a=2 m/s^2. Everything feels heavier, as if the gravitational constant would be g'=g+2 instead of 10 m/s^2. Even the buoyant force will be larger than in the tank in rest.

Can you proceed?

ehild

5. Dec 16, 2011

### vkash

yes i have read this in starting mechanics.(working with non inertial frame of reference)
B=M(g+a)+T
Is it correct?

if string is snapped.
B-m(g+a)=ma'

6. Dec 16, 2011

### ehild

I hope It will be OK if you calculate the buoyant force correctly.

ehild

7. Dec 16, 2011

### vkash

volume of ball is 2/500=4*10-3
B=(4*10-3)*(10)*(1000)
here i did it wrong.
It should B=(4*10-3)*(10+2)*(1000)
thanks ehild. I got the mistake.

8. Dec 16, 2011

Well done!

ehild