To solve this problem, we need to understand how the intensity of the gravitational field $(E)$ varies with distance $(r)$ from the center of the Earth.$\\$1. Inside the Earth $(r < R): \\$• The gravitational field intensity $E$ is directly proportional to $r. \\$• This is because the gravitational force inside a uniform sphere is due to the mass enclosed within radius $r. \\ E = \frac{G M_r}{r^2} = \frac{G \left(\frac{M}{R^3}\right) r^3}{r^2} = \frac{G M r}{R^3} \\$• Therefore, $E \propto r. \\$2. On the surface and outside the Earth $(r \geq R): \\$• The gravitational field intensity $E$ follows the inverse square law.$\\ E = \frac{G M}{r^2} \\$• Therefore, $E \propto \frac{1}{r^2}. \\$Now, let's analyze the options:$\\$Option 1:$\\$• Shows a linear increase of $E$ with $r$ inside the Earth, reaching a maximum at $R. \\$• Then, $E$ decreases following an inverse square law beyond $R. \\$• This matches our analysis.$\\$Option 2, 3, and 4:$\\$• Do not correctly represent the linear increase inside the Earth or the inverse square decrease outside.$\\$Therefore, the correct option is Option 1.