Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: R

There are no items in this cart.
Continue Shopping
rajan jha Grade: 12
        A circular lamina of radius a and centre O has mass per unit area kx^2,where x  is the distance from O and k is a constant.If the mass of the lamina is M,find hn terms of M and a, the moment of inertia of the lamina about an axis thrgh O and perpendicular to the lamina.
6 years ago

Answers : (1)

vikas askiitian expert
510 Points

consider a circular lamina placed in xy plane whose center lies ot origin...

mass per unit area (d) is given =kx^2

consider a small element of lamina ...let it be a ring of radius x and thickness dx which is co axial to the lamina...

length of this element =dl=2pix

area of this element is 2pixdx...............1

mass of dis element is dm=(area).(mass per unit area)=2pixdx(d)


moment of inertia of this element about a axis passing through its center and perpendicular

to plane of  element is given by dI=dmx^2

                                              dI =2pikx^5dx.........3

total moment of inertia is equla to integral dI limit from 0 to a

I=2pik (x^6/6) lim 0 to a

I = (pika^6)/3 ..............4

we have eq 2 as dm=2pikx^3dx

 if we integrate this eq then it will give the total mass of lamina (M)

 M=integral(2pikx^3)dx  limit 0 to a


solving 4 and 5 

     I=2/3 ma^2     ans

6 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies
  • Complete Physics Course - Class 12
  • OFFERED PRICE: R 2,600
  • View Details
  • Complete Physics Course - Class 11
  • OFFERED PRICE: R 2,800
  • View Details

Ask Experts

Have any Question? Ask Experts

Post Question

Answer ‘n’ Earn
Attractive Gift
To Win!!! Click Here for details