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Grade: 12th pass

                        

Three identical thin rods each of length l and mass M one joined to form a letter H. If the H so formed is followed to fall from rest so as to allow it to rotate about one of the side, then what will be its angular velocity, when the plane of H is vertical..?

6 years ago

Answers : (10)

Vikas TU
13786 Points
							mgl/2 + mgl = 1/2 x (0 + ml^2/3 + ml^2) x w^2
 solve it and get w (angular velocity.
						
6 years ago
Vikas TU
13786 Points
							plz approve!
						
6 years ago
karunyaa
10 Points
							sorry couldnt get it can you plz explain it briefly
						
6 years ago
Harsh davda
41 Points
							FIRST OF ALL, moment of inertia about one of its side will be the addition of moment of inertia of each rod about the side..   hence now moment of inertia about the first rod about its own axis is zero because its radius is zero.. now MOI of the second rod about its end is Ml²/3 and that of the third rod about the first is Ml² hence moment of inertia of the body is 4Ml²/3  .....  now  torque of gravitational force on the body is R*F=Mgl/2..... weknow that...
T=?a  hence   Mgl/2=4Ml²/3 a ......  which gives a=3g/8l..... now as  
a=vdv/ds .....,,  a=?d?/d?.....   hence... ?d?=(3g/8l).d? ....integrating both the sides..., we get ... ?²/2=3g?/8l.....putting limits.. ?²/2=3g?/16l ...... ?=v(3g?/8l)... whichis ur answer

  thanks,
 regards,
 HD.
						
6 years ago
Harsh davda
41 Points
							FIRST OF ALL, moment of inertia about one of its side will be the addition of moment of inertia of each rod about the side.. hence now moment of inertia about the first rod about its own axis is zero because its radius is zero.. now MOI of the second rod about its end is Ml²/3 and that of the third rod about the first is Ml² hence moment of inertia of the body is 4Ml²/3 ..... now torque of gravitational force on the body is R*F=Mgl/2..... weknow that...
T=Ia hence Mgl/2=4Ml²/3 a ...... which gives a=3g/8l..... now as 
a=vdv/ds .....,, a=wdw/d§..... hence... wdw=(3g/8l).d§ ....integrating both the sides..., we get ... w²/2=3g§/8l.....putting limits.. w²/2=3g(pi)/16l ...... w=v(3g(pi)/8l)... whichis ur answer

thanks,
regards,
HD
						
6 years ago
karunyaa
10 Points
							thank you so much noe i am clear
						
6 years ago
karunyaa
10 Points
							but how come the limit is pi/2?
						
6 years ago
Harsh davda
41 Points
							it was initially horizontal... finnaly became vertical..!
						
6 years ago
karunyaa
10 Points
							oh thankz
						
6 years ago
Ashish Garg
34 Points
							
Three identical thin roda each of length l and mass M are joined together to form a letter H. The moment of inertia of the system about one of the outer sides of H is :-
4 years ago
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