A solid sphere is projected up along an inclined plank of inclination `theta=30^@` with a speed `v=2ms^(-1)`. If it rolls without slipping find the maximum distance traversed by it (`g=10 ms^(-2))`

Explanation

To solve the problem of a solid sphere projected up an inclined plane, we can follow these steps:

### Step 1: Understand the scenario
We have a solid sphere projected up an inclined plane with an inclination angle of \( \theta = 30^\circ \) and an initial speed \( v = 2 \, \text{m/s} \). The goal is to find the maximum distance \( s \) that the sphere travels up the incline before it comes to rest.

### Step 2: Apply the Work-Energy Theorem
The work-energy theorem states that the work done by all forces acting on an object is equal to the change in its kinetic energy. In this case, the work done by gravity will be equal to the change in kinetic energy of the sphere.

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