This is a funny question from my physics book University Physics
by Young & Freedman.
22.29 A negative charge -Q is placed inside the cavity of a hollow metal
solid. The outside of the solid is grounded, by connecting a conducting
wire between it and the earth.
a) Is there any excess charge induced on
the inner surface of the piece of metal? If so, find its sign and
magnitude.
b) Is there any excess charge on the outside of the piece of
metal? Why, or why not?
c) Is there an electric field in the cavity?
Explain.
d) Is there an electric field within the metal? Why, or why not?
Is there an electric field outside the piece of metal? Explain why or
why not.
e) Would someone outside the solid measure an electric field
due to the charge -Q? Is it reasonable to say that the grounded conductor
has shielded the region from the effects of the charge -Q? In
principle, could the same thing be done for gravity. Why or why not?
The answer key is equally funny: yes, +Q; no; yes; no, no; no, yes, no.