Four thin uniform rods, each of length L and mass M are joined to form a square. The moment of inertia of square about an axis along one of its diagonal is
A
ML26
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
4ML23
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
3ML24
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
2ML23
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution
The correct option is D2ML23 The given condition can be shown as
From Perpendicular axis theorem, Iz=Ix+Iy
Since, due to symmetry Ix=Iy ⇒Iz=2Ix or, Ix=Iy=Iz2
Now, for a single rod (say BC), ICOM=ML212
Also, from parallel axis theorem we have Iz=ICOM+Md2 ⇒Iz=ML212+M×(L2)2=ML23
Similarly, for four rods Iz=4×ML23=4ML23
Hence, the moment of inertia of square about an axis along its one diagonal is Ix=Iy=Iz2=(4ML23)2=2ML23