A non-homogenous sphere of radius `R` has the following density variation.
`rho = rho_(0), r le r//3 `,
` rho = rho_(0)//2, (R )/(3) lt r le 3 (R )/(4)`,
`rho = (rho_(0))/(8), (3R)//(4) lt r le R`,
What is the gravitational field due to sphere at distance `2R` from center?

Explanation

To find the gravitational field due to a non-homogeneous sphere at a distance of \(2R\) from its center, we will follow these steps:

### Step 1: Understand the Density Variation
The density of the sphere varies as follows:
- \( \rho = \rho_0 \) for \( r \leq \frac{R}{3} \)
- \( \rho = \frac{\rho_0}{2} \) for \( \frac{R}{3} < r \leq \frac{3R}{4} \)
- \( \rho = \frac{\rho_0}{8} \) for \( \frac{3R}{4} < r \leq R \)

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