the MI is same abt. all the axes and is equal to 2/3MR^2... abt. each axis, you can imagine another hemisphere of equal mass..which when combined withthe one already present gives a hollow sphere of mass 2*m.
the moment of inertia of both these hemispheres abt the axis is same and say equal to I.
SIR PLEASE SOLVE THE PROBLEM GIVEN BELOW PLEASE!! A child of mass m sits in a swing of negligible mass suspended by a rope of length l. Assume that the dimensions of the child are negligible compared with 1. His father pulls the child back until the rope makes an angle of one radian with vertical, then pushes with a force F=mg along the arc of the circle releasing at the vertical : a) How high up will the swing go? b) How long did the father push?
it should be 2/5 MR^2 along each axis
ReplyDeleteyes 2/5 MR^2
ReplyDeletei thought you might fall for it..you're right.
ReplyDeleteisnt it a hollow hemisphere?it should be 2/3 MR^2
ReplyDeletesorry 2/3 MR^2
ReplyDeletethe best way is to treat such questions is as done in module
just break a sphere in 2 parts
i fell for it!..that the perpendicular axis theorem is valid for only plane bodies slipped out of my mind..
ReplyDeletewhat is the answer guys with explanation please
ReplyDeletewhat is the answer guys with explanation please
ReplyDeletethe MI is same abt. all the axes and is equal to 2/3MR^2...
ReplyDeleteabt. each axis, you can imagine another hemisphere of equal mass..which when combined withthe one already present gives a hollow sphere of mass 2*m.
the moment of inertia of both these hemispheres abt the axis is same and say equal to I.
then 2I=2/3(2m)R^2.
hence..you find I!
SIR PLEASE SOLVE THE PROBLEM GIVEN BELOW PLEASE!! A child of mass m sits in a swing of negligible mass suspended by a rope of length l. Assume that the dimensions of the child are negligible compared with 1.
ReplyDeleteHis father pulls the child back until the rope makes an angle of one radian with vertical, then pushes with a force F=mg along the arc of the circle releasing at the vertical :
a) How high up will the swing go?
b) How long did the father push?
ans:(a) theta=63degree above horizon (b) t=1.52(l/g)^1/2