Question bank/JEE Main/Physics

JEE MainPhysicsModerateRigid Body Dynamics

A sphere of mass m is given some angular velocity about a
horizontal axis through its centre, andgently placed on a plank of mass
m. The coefficient of friction between the two is μ\mu. The plank rests
on a smooth horizontal surface. The initial acceleration of the sphere
relative to the plank will be x(μg)x(\mu g). Find the value of x.

Show answer and solution
asphere  =μmgm=μg(+i^)a_{sphere\ \ } = \frac{\mu mg}{m} = \mu g( + \widehat{i})
aplank  =μmgm=μg(−i^)a_{plank\ \ } = \frac{\mu mg}{m} = \mu g\left( - \widehat{i} \right)
 arelative  =2μg{\ a}_{relative}\ \ = 2\mu g

Source: Grass-G / P-07 Physics paper 17 October.docx

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