two spheres (Issac physics) statics level 6

I got 16.1 for the question but it says it's incorrect.
The question is like this:
https://isaacphysics.org/questions/two_spheres?board=b212f0eb-bab0-477a-ad0f-dd5471f67b58&stage=a_level

two spheres with radii 8r and 4r, mass 4mg and mg and in contact with a force 2mg applying at the top of the big sphere. the system is in equilibrium. the first question asks the normal reaction on the ground to the big sphere. I resolved all the forces and got 16.1 for several times.... but it's wrong could anyone help with me pleasessss!

Thanks so much!

The hints about making the moment zero in equilibrium is the way to go as its avoids the need to directly calculate the spheres interactions. So try taking moments about the spheres contact point. Upload what youve done if you can't get it.

thank you very much. I used c as the pivot, so like 4mg*7.54= N*7.54+2mg*10.67, I got N=5.73 but it's still not correct... would you like to give some other hints pls

oh thank you I got 5.75!

oh thank you I got 5.75!

https://isaacphysics.org/questions/closest_approach_nucleus?board=f90ccb4d-fb36-4cfb-b8cb-eab472dd514f&stage=a_level

would you like to have a look of this question as well pls... I got 8.90e-13 and the question says I should consider conservation of momentum and energy, so I calculated the velocity of the alpha particle and gold nucleus when they are at the closet distance and I 6.05e-11 for the closet distance but it's wrong..
I haven't studied electric field yet,,,, thanks so much!!

Can you upload a pic of your calculations? Its easier to help if I don't have to guess what you've tried to do.

Youve not included the calcs before the top of the page, but assuming the KE at the top is the KE prior to the collision, you should really use the change in KE.

I got 9.03e-13 but it's still incorrect

Yup. I guess you "balanced" horizontal forces originally for the large sphere then projected onto the vertical? Its probably worth spending a bit of time in understanding the rough sphere / surface statement and why they get you to show that F (surface friction for the large sphere) is zero initially.

thank you very much. I used c as the pivot, so like 4mg*7.54= N*7.54+2mg*10.67, I got N=5.73 but it's still not correct... would you like to give some other hints pls

How did u get 7.54 for 8sintheta if u could explain please ?

Yup. I guess you "balanced" horizontal forces originally for the large sphere then projected onto the vertical? Its probably worth spending a bit of time in understanding the rough sphere / surface statement and why they get you to show that F (surface friction for the large sphere) is zero initially.

What have you tried to do (upload a sketch?), what do you think it should be?

I balanced forces for both spheres, and each sphere, and used moments about C but am struggling to find an expression for the angle theta, and how friction under A is 0

For the taking moments, by theta I presume you mean the angle that the line between the centres (through the contact point C) makes with the horizontal? It should be fairly clear what sin is and hence what cos is using pythagoras? You don't need the actual angle, only the trig side ratios.

yes exactly that, what values should I use.