Calculate the gravitational field intensity at the centre of the base of a hollow hemisphere of mass `M` and radius `R`. (Assume the base of hemisphere to be open)
Text Solution
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We consider the shaded elemental ring of mass `dm=M/((2piR^(2)))2piRsintheta(Rd theta)` Field due to this ring at `O` `dE=(GdmRcostheta)/(R^(3))` (see formulae for field due to a ring) or `dE=(GM)/(R^(2)) sinthetacosthetad theta` Hence `E=int_(0)^(pi//2) dE=int_(R^(2))^(pi//2) (GM)/(R^(2))sinthetacosthetad theta` or `E=(GM)/(2R^(2))`
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