# Newton's Laws of Motion - Two spheres in a cup [closed]

This is the question I got really confused over:

I tried drawing the free body diagram of the sphere on the left.

Now if we let the angle between the vertical plane and $$N_1$$ be $$\theta$$, this implies $$N_1\sin(\theta)=N_2$$

It seems from the diagram that since the radius of the cup is $$3r$$, $$\sin(\theta)=\frac{1}{3}$$.

That would mean the ratio of the two forces is $$3$$.

But it seems that the answer is $$2$$.

Can you tell me what was wrong with my approach or what is the right approach to this problem?

• Hi Abi Nand! Welcome to Physics SE. A couple of things: One is not supposed to paste pictures of whole questions--it is fine to paste relevant diagrams as pictures but reproduce the rest of the question as text. Also, for mathematical expressions, one is supposed to use MathJax. Cheers! :) May 18 '19 at 3:19
• Apart from the formatting issues that I pointed out in my previous comment, please notice that you should ask a question that is really a question about physics, i.e., some conceptual point that you might be confused about. Your current question is simply asking one to figure out what is wrong with your solution as it doesn't seem to match the answer provided in the book it seems. Thus, I am voting to close the question. May 18 '19 at 3:25
• sin theta= 1/2. May 18 '19 at 3:27
• Ishan Jawale - How is sin theta = 1/2. The radius of the cup is 3r and the radius of the ball is r. May 18 '19 at 3:37
• The radius of the cup may be $3r$, but note the right angle triangle that has one of its points through the centre of one sphere (not the point where the sphere makes contact with the cup) May 18 '19 at 8:15

## 1 Answer

Read the question without looking at the misleading diagram. $$3r$$ isn't the distance from the origin of each sphere to the origin of the cup. $$3r$$ is the distance from the origin of the cup to the points where each sphere touches the cup. That's $$r$$ longer than the distance from the origin of the cup to the origin of each sphere. The distance from the origin of the cup to the origin of each sphere is merely $$2r$$.

The diagram is drawn with incorrect proportions. The spheres are drawn too small relative to the cup. If you redraw the picture with correct proportions from your imagination, without looking at the misleading diagram, you'll find that the distance from the origin of a sphere to the origin of the cup is a mere $$2r$$. Thus the answer is 2.