Question

A spherical hole is made in a solid sphere of radius R. The mass of the sphere before hollowing was M. The gravitational field at the centre of the hole due to the remaining mass is

• A. Zero
• B. $\frac{GM}{8R^2}$
• C. $\frac{GM}{2R^2}$
• D. $\frac{GM}{R^2}$

Answer 1

The correct option is C

$\frac{GM}{2R^2}$

By the principle of superposition of fields

${}_E^{\to }{=}_{E_1}^{\to }{+}_{E_2}^{\to }$

Here ${}_E^{\to }$ = net field at the centre of hole due to entire mass

${}_{E_1}^{\to }$ = field due to remaining mass

and ${}_{E_2}^{\to }$ = field due to mass in hole = 0

$\therefore E_1=E=\left(\frac{GM}{R^3}\right).rwherer=\frac{R}{2}\therefore E=\frac{GM}{2R^2}$