Question bank/JEE Main/Physics

A sphere of mass is given some angular velocity about a
horizontal axis through its centre and gently placed on a plank of mass
The co-efficient of friction between sphere and plank
is[IMAGE]. The plank rests on a smooth horizontal
surface. The initial acceleration of the centre of sphere relative to
the plank will be

AZero

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FBD for sphere & block
$a_{2} = \frac{f_{r}}{m} = \frac{\mu mg}{m}$
${\overrightarrow{a}}_{1} = \mu g\overset{\hat{}}{i}$
${\overrightarrow{a}}_{2} = - \mu g\overset{\hat{}}{i}$
${\overset{\rightarrow}{a}}_{rel} = {\overset{\rightarrow}{a}}_{1} - {\overset{\rightarrow}{a}}_{2} = 2\mu g\overset{\hat{}}{i}$
$a_{rel} = 2\mu g$.

Source: Grass-G / P-10 Physics paper 1 30 October Jee Main.docx