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 –Fig.

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

Answer 1

Answer: (C)

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

Answer 2

By the principle of superposition of fields

=+

Here, = net field at the centre of hole due to entire mass

= field due to remaining mass

and = field due to mass in hole = 0

\ ==.r

where r =

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