Question

A uniform solid sphere of mass $M$ and radius a is surrounded summetrically by a uniform thin spherical shell of equal mass and radius $2\text{a}$. What will be the gravitational field at a distance $\frac{5}{2}$ a from the centre?

• A. $\frac{4}{9}\frac{GM}{a^2}$
• B. $\frac{8}{25}\frac{GM}{a^2}$
• C. $\frac{4}{16}\frac{GM}{a^2}$
• D. Zero

Answer 1

The correct option is B $\frac{8}{25}\frac{GM}{a^2}$


$\begin{array}{cc}{\overrightarrow{E}}_{\text{net}}& ={\overrightarrow{E}}_{SS}+{\overrightarrow{E}}_{HS}\\ & =\frac{GM}{r^2}+\frac{GM}{r^2}\end{array}$

$E_{net}=\frac{G\left(2M\right)}{{\left(\frac{5a}{2}\right)}^2}=\frac{8GM}{25a^2}$