MHT CET · Physics · Gravitation

A uniform solid sphere of mass ' m ' and radius ' r ' is surrounded by a uniform thin spherical shell of radius ' \(2 r\) ' and mass ' \(m\) ' then the gravitational field

A at a distance of 15 r from the centre is \(\frac{2}{9} \frac{\mathrm{Gm}}{\mathrm{r}^2}\)
B at a distance of \((2 \cdot 5) \mathrm{r}\) from the centre is \(\frac{8}{25} \frac{\mathrm{Gm}}{\mathrm{r}^2}\)
C at a distance of \((1 \cdot 5) \mathrm{r}\) from the centre is zero.
D between the sphere and spherical shell is uniform.

Verified Solution

Answer & Solution

Correct Answer

(B) at a distance of \((2 \cdot 5) \mathrm{r}\) from the centre is \(\frac{8}{25} \frac{\mathrm{Gm}}{\mathrm{r}^2}\)

Step-by-step Solution

Detailed explanation

At \( x = 2.5r \), which is \( x > 2r \). \( E = \frac{2 G m}{x^2} \)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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