Question

The direction of gravitational intensity at point p of a hemispherical shell of uniform mass density is indicated by the arrow:

• A. d
• B. e
• C. c
• D. r

Answer 1

Answer: (C)

c

we know, the gravitational intensity due to a body at a point is the force acting per unit mass on a body at that point. it is a vector quantity and its direction is same as direction of force on unit mass.we also know, if we take a uniform spherical shell, at each point inside the hollow spherical shell, Gravitational field intensity will be zero as Various regions of the spherical shell attract the point mass inside it in various directions. These forces cancel each other completely. Now the shell is spherically symmetric so if the upper half of shell, pulls a point mass towards it with the magnitude of Force ‘F’ so same with the amount of force lower half of shell will pull it as shown in 1st figure

So if we remove the upper half of sphere there will force acting on point mass will be in a downward direction only, so that will be the direction of field intensity as shown by $\left(C\right)$ in the 2nd figure