wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A long metal rod of length l and relative density σ is held vertically with its lower end just touching the surface of water. The speed of the rod when it just sinks in water is given by


A

2gl

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

2glσ

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

2gl(112σ)

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

2gl(2σ1)

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

The correct option is C

2gl(112σ)


Let the densities of metal and water be ρ and ρ0 respectively and let x be the length of the rod immersed in water at an instant of time t. Then, acceleration at that instant = apparent weight divided by mass of the rod, i.e.
dvdt=πr2lρgπr2xρ0gπr2lρ=ggxρ0lρ=g(1xσl)
dvdx.dxdt=g(1xσl)
vdvdx=g(1xσl)
Integrating, we have
v22=gxx22σll0=gl(112σ)
v=2gl(112σ)
Hence, the correct choice is (c).


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