Find the accelerations `a_1,a_2,a_3` of the three blocks shown in figure if a horizontal force of 10 N is applied on a. 2 kg block, b. 3 kg block, c. 7 kg block. Take `g=10 m/s^2`.

Explanation

Given
`mu_1=0.2 mu_2=0.3 mu_3=0.4`

a. Whenthe 10N force is aplie don 2 kg blcok, it experiences maximum frictioN/Al froce.
`muR_1=muxx2g=(0.2)xx20`
`=4N from the 3 kg blocl So, the 2 kg block experience a net froce `=10-4=6N`
So,` a_1=6/2=3m/s^2`
But for the 3 kg block, ure the frictioN/Al force from 2 kg block (4N) becomes the driving force and the maximum frictioN/Al foce between 3 kg and 7 kg blocks
`mu_2=RP_2=(0.3)xx5 kg`
=15N
S, the 3 kg block cannot move relative to the 7 kg block, the 3 kg blcok and the 7 kg block bothwill have same acceleration`(a_2=a_3)` which will be due to the 4N force because there is no friction from the floor.
`a_2=a_3=4/10=0.4m/s^2`
b. When the 10 N force is appied to the 3 Kg block, it canexperience maximum frictioN/Al force of 15+4=19N fromthke 2 kg block and 7 kg blcok.
So, it can not move with respect to them. As tehfloor is frictionless, al the three bodies will move together.
`:. a_1=a_2=a_3=10/12=(5/6)m/s^2.