MHT CET202523 Apr 2025Morning ShiftPhysicsGravitationActual
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
Options
- Aat a distance of 15 r from the centre is 2 9 Gm r ^2
- Bat a distance of (2 5) r from the centre is 8 25 Gm r ^2
- Cat a distance of (1 5) r from the centre is zero.
- Dbetween the sphere and spherical shell is uniform.
Correct answer
B. at a distance of (2 5) r from the centre is 8 25 Gm r ^2
Step-by-step solution
The gravitational field at any point results from superposition of contributions from the solid sphere and spherical shell, each with mass m . For a solid sphere of radius r : inside ( d At distance 1.5r from center, the point lies outside the sphere ( 1.5r > r ) and inside the shell ( 1.5r At distance 2.5r from center, the point lies outside both distributions. Hence E_ total = Gm (2.5r)^2 + Gm (2.5r)^2 = 8 25 Gm r^2 , confirming option B. In the region between sphere and shell ( r Final answer: B