Question
Download Solution PDFA sphere of mass m and radius r << R is placed inside a rotating horizontal cylinder of radius R. As the cylinder's angular acceleration, β, gradually increases, find the maximum value of β that enables the sphere to reach from A to the horizontal point B.
- 2g/R
- 5g/R
- (2g) / (5R)
- (5g) / (2R)
Answer (Detailed Solution Below)
Option 4 : (5g) / (2R)
India's Super Teachers for all govt. exams Under One Roof
FREE
Demo Classes Available*
Enroll For Free Now
Detailed Solution
Download Solution PDFConcept Used:
A small sphere of mass m and radius r is placed inside a rotating horizontal cylinder of radius R . The sphere undergoes pure rolling motion inside the cylinder due to friction.
Calculation:
Applying the rolling condition:
⇒ β(R-r) = (g sinθ + β(R-r)) / (1 + 2/5)
⇒ (7/5) β(R-r) - β(R-r) = g sinθ
⇒ θ = sin⁻¹ (2β(R-r) / 5g)
The maximum angular acceleration (β) required for the sphere to reach point B is:
⇒ β = (5g) / (2R)
Correct Option: Option 4
India’s #1 Learning Platform
Start Complete Exam Preparation
Daily Live MasterClasses
Practice Question Bank
Mock Tests & Quizzes
Trusted by 7.2 Crore+ Students