For the thin rod of mass m shown in the figure, choose the correct statement(s) regarding moment of inertia about the axis 1,2,3,4. Here axis 4 is passing through the centre of the rod.
A
M.O.I about axis 1 is zero.
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
M.O.I about axis 2 is mL23
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
M.O.I about axis 3 is 13mL212
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
M.O.I axis 4 is mL212
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution
The correct options are AM.O.I about axis 1 is zero. BM.O.I about axis 2 is mL23 CM.O.I about axis 3 is 13mL212 DM.O.I axis 4 is mL212 About axis 1, Using I=mr2, as r=0 I1=mr2=0
About axis 2, Using parallel axis theorem I=I0+md2 I=mL212+mL24 ⇒I=mL23 [∵d=L2]
About axis 3, Similarly as in case of axis 2, using the same parallel axis theorem and putting d=L ⇒I=I0+mL2=13mL212
About axis 4, ∵ Axis 4 is through centre of mass of rod. I4=I0=mL212 [about axis passing through centre of mass] ⇒I4=mL212 ∴ All of the above options are correct.