Question

hii friends plzz plzz give me answer ❤☺❤❤☺❤☺
solve this step by step..❤❤

Answer 1

Since we do not know that whether the plate and body move together or not, we make assumptions as follows:
Treating both the blocks as a system moving with acceleration $a$ we get,
$3\mu mg=(M+m)a\\ \Rightarrow a=\dfrac{3\mu mg}{m+M}$
To check the validity of our assumption let us calculate the frictional force $f$. Consider the plate,
$f=Ma\\ =3\dfrac{\mu mMg}{M+m}\\ =3\mu mg\left(1+\dfrac{M}{m}\right)>3\mu mg>\mu mg=\mu \mathcal{N}$
Since, the static friction does not exceed $\mu \mathcal{N}$, our assumption is incorrect.
This means that the body is sliding relative to the plate and therefore kinetic friction is present.
Now, consider the plate again,
$f=Ma\\ \Rightarrow \mu mg=Ma\\ \Rightarrow a=\dfrac{\mu mg}{M}$