## Goldman Sachs Interview Question

Financial Software Developers**Country:**United States

**Interview Type:**Phone Interview

Airplane is a vehicle , so we can go the over the list of all materials used and their specifications and get the total weight. Not a very smart answer , but I think not a bad one too...

As it is a well known fact that anything immersed in water displaces an equal amount of water as of its weight ...so putting the plane inside water and weighing the water displaced by it will give the plane's weight.

I was also asked same question by GS, but interview kept on asking what else other approach can you think of. But i couldn't give the answer he was looking for.

I searched on internet and found the solution, which was put plane on a ship which is in water and mark the hull immersed in water, then remove the plane from ship and start loading ship with known weights and the weight with which ship's hull comes to same marked position is the weight of plane.

Use a rope and try to just move the aeroplane while measuring the power consumed by the vehicle trying to move the plane...now from this you can calculate the force that was required to just move the plane. Now calculate the coefficient of friction of the tyre using a model. Now you know the force needed to move the plane and the coefficient of friction use this to calculate the wieght of the plane

Just pull the plane with a known force. say F. Calculate the velocity of the plane. Then neglecting force of friction.

F = 1/2(m)v^2

as initial PE being 0.

calculate m. weight will be m*9.794 i.e m*g (g being 9.794 in delhi). Best and the most practical way.

To calculate exact weight (not rounding off the co-efficient of friction)

Pull the plane with different forces F1 and F2 (F1>F2)

The equations would be as follows

F1=Work done by friction + 1/2(m)(v1)^2

F2=Work done by friction + 1/2(m)(v2)^2

Work done by friction will be constant in both cases as co-efficient of friction and normal force does not change

now take the diff

F1-F2=1/2(m)(v1)^2-1/2(m)(v2)^2

we know F1,F2,v1 and v2 and calculate m

Assumptions: Force F is applied along the centre of mass of plane so that it does not interfere with normal force.

Calculating the weight based on friction is doubtful for me. I mean suppose if the plane is on wheels and we apply a force F the velocity will be higher compared to the same force applied when there are no wheels in plane. In case there are no wheels the friction will be more. These factors should be considered?

1. Component weight

2. Water displacement theory

3. Newton law of f=m/a -Apply a constant force and get an acceleration.. then get the weight which would be approx.

4. Tyre pressure thing

5. Get a prototype of the same specification, same set of components and determine its weight.. Once determined, scale up to the original specification ratio

Some weird ways that I can think of:

1) Attach the aeroplane on to a giant spring, and let it oscillate. Find period of oscillation and solve the equation for mass thereafter.

2) Throw the aeroplane from a certain height. Let it hit the ground on a pressure measuring device. Then get force and solve for mass using 'g'.

3) Use the aeroplane as a 'hammer' - yes, which is used in hammer throws. Tie it to a large enough 'rotating' device. Throw the aeroplane into the air at a certain velocity. Measure the distance from the point of throw to point of fall. Get the force from that and solve for mass thereafter.

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Here is the right answer, but could not think of when i was asked this question

- OTR August 06, 2013Put plane on a ship which is in water and mark the hull immersed in water, then remove the plane from ship and start loading ship with known weights and the weight with which ship's hull comes to same marked position is the weight of plane.