wiz-icon
MyQuestionIcon
MyQuestionIcon
6
You visited us 6 times! Enjoying our articles? Unlock Full Access!
Question

Consider a rope of total mass M and length L suspended at rest from a fixed mount. The rope has a linear mass density that varies with height as λ(z)=λ0sin(πzL), where λ0 is a constant. Constant gravitational acceleration g acts downward, then constant λ0 is

A
πM2L
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
πM3L
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
πM4L
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
2πML
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A πM2L
Consider the rod as

We consider length of the rod from bottom to top.
We have been given that
λ=λ0sin(πzL)
dmdz=λ0sin(πzL)
M0dm=L0λ0sin(πzL)dz
M=λ0Lπ[cos(πzL)]L0
M=λ0Lπ[1+1]
λ0=πM2L

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Springs: Playing with a Slinky
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon