1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Four particles each of mass 500 g are placed at the four corners of a rectangle ABCD with sides of length 5 m and 10 m. What is the ratio of moment of inertia of the system when AB is the axis to when BC is the axis?

A
1:4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
2:1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
1:2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
4:1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

## The correct option is D 4:1 When AB is the axis of rotation, rD=AD=10 m, rC=BC=10 m mA=mB=mC=mD=500 g=0.5 kg Moment of inertia of system of particles about AB, ⇒IAB=IA+IB+IC+ID IAB=mAr2A+mBr2B+mCr2C+mDr2D IAB=0.5×0+0.5×0+0.5×102+0.5×102 ∴IAB=100 kg- m2 When BC is the axis of rotation, r′A=AB=5 m,r′D=DC=5 m Moment of inertia of system of particles about BC, ⇒IBC=IA+IB+IC+ID ⇒IBC=mAr′2A+mBr′2B+mCr′2C+mDr′2D IBC=0.5×52+0.5×0+0.5×0+0.5×52 ∴IBC=12.5+12.5=25 kg -m2 ⇒IABIBC=10025=4:1 Hence the correct option is (d).

Suggest Corrections
0
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program