A force of magnitude F acting up and along a smooth inclined plane, can support a mass M in equilibrium. If a force of the same magnitude acts horizontally, it can support a mass m on the same inclined plane in equilibrium.

Find a relationship between F, M and m which is independent of the angle of inclination of the slope.

 

Im not so sure on this one... I guess you:
Take each force and particle separately.
Resolve the forces into horizontal/vertical components.
Let the sum of all these forces equal 0.
Do the same for the second particle and equate the two equations to each other through F.

Good so far?

Looks good so far. Whatever angle is used on the incline has to cancel somewhere in your solution.

Thank you Just making sure before I progress through it

 

Resolve the forces into horizontal/vertical components

 

It is often less calculation effort to resolve parallel and perpendicular to the plane in inclined plane problems.

 

This is part of a more general principle where we resolve in directions perpendicular to some of the unkowns and take moments about points they pass through.

Sorry, I may have been unclear.

 

I think I was referring to the same thing you are... But you used the correct terminology

Resolving vertically and horizontally will work, it just introduces extra terms into the equations.

There are always lots of ways of performing the calculations.

It is a valuable skill to be able to spot the easy one.