Consider two solid spheres of radii R₁ = 1m, R₂ = 2m and masses M₁ and M₂, respectively. The gravitational field due to sphere (1) and (2) are shown. The value of M₁/M₂ is :

Solution

Physics sir · 3 steps

Read the peak of each graph: that peak is the surface field GM/R², so mass is field times R².

1. Where the peak sits. Inside a solid sphere the field grows linearly with distance. Outside it falls as 1/r². So each graph peaks exactly at the surface, r = R.

   E_(surface) = GM/R² ⇒ GM = E_(surface) R²

2. Read the graph. Sphere (1) peaks at E = 2 at R₁ = 1 m, so GM₁ = 2 × 1² = 2. Sphere (2) peaks at E = 3 at R₂ = 2 m, so GM₂ = 3 × 2² = 12.
3. So. M₁/M₂ = 2/12 = 1/6, which is option (b).

The idea to keep. The kink in an E vs r graph for a solid sphere marks its surface. The peak value there is GM/R², so always multiply by R² before comparing masses.

Answer from the NTA final answer key. Solution by PrepWiser.