wiz-icon
MyQuestionIcon
MyQuestionIcon
10
You visited us 10 times! Enjoying our articles? Unlock Full Access!
Question

A uniform rod of mass m and length l is released from rest in the vertical position on a rough (surface is sufficiently rough to prevent sliding) square corner A, shown in figure, then choose correct options: (given that normal acts along the length of the rod)

A
If the rod just begins to slip when θ=37 with vertical, then the coefficient of static friction μ between the rod and the corner is 0.3.
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
If the end of the rod is notched so that it cannot slip, then the angle θ at which contact between the rod and the corner ceases is 53
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
If the rod just begins to slip when θ=37 , then the coefficient of static friction μ between the rod and the corner is 34
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
If the end of the rod is notched so that it cannot slip, then the angle θ at which contact between the rod and the corner ceases is 37.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct options are
A If the rod just begins to slip when θ=37 with vertical, then the coefficient of static friction μ between the rod and the corner is 0.3.
B If the end of the rod is notched so that it cannot slip, then the angle θ at which contact between the rod and the corner ceases is 53

Using conservation of energy
mgl2=mg(l2)cosθ+12(ml23)ω2
ω2l2=3g2(1cosθ)....(1)
Using Newton's second law along the rod
mgcosθN=mω2(l2)
N=mgcosθm3g2(1cosθ)......(2)
N=mg2(5cosθ3)
Torque equation about point of contact
(mgsinθ)l2=ml23α
α=3gsinθ2l...(3)
Using Newtons second law perpendicular to rod,
mgsinθfs=m(l2)α....(4)
mgsinθfs=m(l2)3gsinθ2l
fs=mgsinθ4....(4)
When slipping begins
fs=μN.....(5)
mgsinθ4=μmg2(5cosθ3)
when θ=37
μ=0.3
For contact to cease N=0cosθ=35θ=53

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