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A body of mass m is kept over an object ...

A body of mass m is kept over an object of mass M. The object is at rest on smooth. Coefficient of static friction between the two bodies is `mu` . What is the minimum force that needs to be applied on the object, so that the body will be about to slip over it?

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Let the force applied on the object horizontally Fig, so that the body is about to slide be F. Hence the common acceleration of the system,
a `= (F)/(M+m),` So the force on the body = ma = `(Fm)/(M+m)` When the body is about to slip this force is balanced by the force of limiting friction acting at the plane of contact.
`:.` Frictional force , f = `mu mg = (Fm)/(m+M)`
or, F`=mu (M+m)g`.
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