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

You are given a rod of length 'L'. The linear mass density varies as λ. λ=a+bx. Here a & b are constants and the mass of the rod increases as x increases. Find the mass of the rod.


A

aL2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

aL+bL22

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

L2(a+b)2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B

aL+bL22


We cannot calculate the mass of the rod by simply multiplying linear mass density 'λ will the length of the rod as λ is not constant.

Hence we have to divide entire rod length into a number of elements and add the mass of all elements.

M=dm1+dm2+dm3+.......

This step can be written in terms of integration.

M=dm

If we take an element dx on the rod at a distance x from the left end of the rod.

Mass of this element dm=λ.dx

dm=(a+bx)dx

Hence total mass M=dmM=L0(a+bx)dx

M=L0a dx+L0bx dx=aL0dx+bL0x dx=a[x]L0+b[x22]L0M=aL+bL22


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Integration
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon