A cube is resting on an inclinded plane. If the angle of inclination is gradually increased. What must be the coefficient of friction between the cube and plane so that,
(a). Cube slides before toppling?
(b). Cube topples before sliding?

Explanation

To solve the problem of determining the coefficient of friction between a cube and an inclined plane such that the cube either slides before toppling or topples before sliding, we can analyze the forces and torques acting on the cube.

### Step-by-Step Solution:

#### Step 1: Identify Forces Acting on the Cube
When the cube is resting on the inclined plane at an angle θ, the following forces act on it:
- Weight (mg) acting vertically downward.
- Normal force (N) acting perpendicular to the inclined plane.
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