# Determine the maximum ratio h/b

1. Sep 12, 2016

### Sanchayan Dutta

Determine the maximum ratio $$h/b$$ for which the homogenous block will slide without toppling under the action of force F.The coefficient of static friction between the block and the incline is $$\mu_s$$.

I have a doubt.About which point should the rotational equilibrium be applied?Should it be applied about centre of mass?Or should it be applied about the vertex opposite to the vertex where F is applied?Why?

**MY ATTEMPT:**

**Translational Equations**
$$F+mg\sin(\theta) \geq \mu N$$
and $$N=mgcos(\theta)$$

**Rotational Equations**
This is where I'm facing a problem.Depending upon which point the equilibrium is applied the required ratio will be obtained.

**MY VIEWS:**

Rotational equilibrium should hold at all points if no toppling/rotation happens.However the answer varies depending on the point of application of equilibrium.Strange.

2. Sep 12, 2016

### haruspex

You are right that it would be strange. As long as you take all relevant forces into account properly, you should get the same answer. You must be making a mistake in one or other of your attempts.