A solid sphere of radius R starts rotating on rough horizontal surface with translational velocity v0 and initial angular velocity ω0=2v0/3R . The sphere starts purerolling after some time t. Find the angle by which sphere rotates upto the instant at which pure rolling starts, if v is the translational velocity at pure rolling. Assume uniformly accelerated motion up to start of pure rolling.
see full answer
Your Exam Success, Personally Taken Care Of
1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.
An Intiative by Sri Chaitanya
a
3338vtR
b
3738vtR
c
3138vtR
d
2937vtR
answer is A.
(Unlock A.I Detailed Solution for FREE)
Best Courses for You
JEE
NEET
Foundation JEE
Foundation NEET
CBSE
Detailed Solution
ω0=2v03R or, v0=32Rω0Angular momentum is conserved about A.Li=Lf ⇒25mR2×2v03R+mv0R=25mR2vR+mvR⇒v0=2119v ...........(i)Now, ω=ω0+αt⇒v/R=2v0/3R+αt⇒α=5v19Rtwhere t is the time in which pure rolling starts.Pure rolling starts when sphere rotates by an angle,θ=ω0t+12αt2=2v03Rt+12⋅5v19Rt⋅t2=3338vtR
A solid sphere of radius R starts rotating on rough horizontal surface with translational velocity v0 and initial angular velocity ω0=2v0/3R . The sphere starts purerolling after some time t. Find the angle by which sphere rotates upto the instant at which pure rolling starts, if v is the translational velocity at pure rolling. Assume uniformly accelerated motion up to start of pure rolling.