A wooden cube is placed on a rough horizontal table, a force is applied to the cube. Gradually the force is increased. Whether the cube slides
before toppling or topples before sliding is independent of :

Wooden Cube: Sliding vs Toppling Analysis

Problem: A wooden cube is placed on a rough horizontal table. A force is applied to the cube and gradually increased. Whether the cube slides before toppling or topples before sliding is independent of what parameter?

Analysis of Forces:

For Toppling:

Mg × (L/2) = F₁ × h

Where L is the cube length, h is the height at which force is applied

For Sliding:

μMg = F₂

Where μ is the coefficient of friction

Condition for sliding to occur first:

F₁ > F₂

Substituting the equations:

(MgL)/2 > μMg

Simplifying by canceling Mg from both sides:

L > 2μh

Key Observation:

Notice that the mass (M) cancels out completely from the inequality!

The condition depends only on:

• Coefficient of friction (μ)
• Cube's length (L)
• Height of force application (h)

Answer:

Whether the cube slides before toppling or topples before sliding is independent of the mass (M) of the cube.

The outcome depends only on the cube's geometry and the friction between the surfaces, not on how heavy the cube is.