CBSE Class 11-science Answered
A sphere of radius 2 m rolls on a horizontal plank.The acceleration of the plank is 2m/s^2 and acceleration of centre of mass of sphere is 4m/s^2 in the direction opposite to that of plank. What is the value of angular acceleration of the sphere?
Asked by suchananag2002 | 01 Nov, 2019, 11:29: AM
Expert Answer
If a sphere is rolling on a moving platform, point of contact has same velocity of moving platform
hence, we have, u = ωR - vCM ......................(1)
where u is velocity of moving platform, ω is angular velocity of rolling sphere , R is radius of sphere
and vCM is velocity of centre of mass of sphere
if we differentiate eqn.(1), we get, du/dt = (dω/dt)R - dvCM/dt = ap = α R - aCM
where ap is acceleration of plank, α is angular acceleration of sphere and aCM is acceleration of centre of mass
hence , α = ( ap + aCM) / R = (2+4)/2 = 3 rad/s
Answered by Thiyagarajan K | 01 Nov, 2019, 02:32: PM
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