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..?

karunyaa, 10 years ago

Grade:12th pass

10 Answers

Vikas TU

14149 Points

10 years ago

mgl/2 + mgl = 1/2 x (0 + ml^2/3 + ml^2) x w^2 solve it and get w (angular velocity.

Vikas TU

14149 Points

10 years ago

plz approve!

karunyaa

10 Points

10 years ago

sorry couldnt get it can you plz explain it briefly

Harsh davda

41 Points

10 years ago

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.

Harsh davda

41 Points

10 years ago

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

karunyaa

10 Points

10 years ago

thank you so much noe i am clear

karunyaa

10 Points

10 years ago

but how come the limit is pi/2?

Harsh davda

41 Points

10 years ago

it was initially horizontal... finnaly became vertical..!

karunyaa

10 Points

10 years ago

oh thankz

Ashish Garg

34 Points

7 years ago

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 :-