does the body get fully immersed in the water and liquid? if yes, then the density of the metal comes out to be 7g/cc(i'm not sure, i might be wrong) ; if no, then i have to think about the question once again....

for part A))

 

if you have a 3rd degree equation like ax³+bx²+cx+d=0 then, let the roots be p,q,r. so, sum of roots(p+q+r) will be the minus of coefficient of x² divided by coefficient x³ i.e. p+q+r= -b/a. which means sum of roots is not always zero(it's zero only if b=0)

moreover, the product of roots i.e. p.q.r=-d/a .

problem solving chart in a company...

 

some more

the solution is as follows.....

 

since on the upper block/slab the force is of 100N which is much more than the limiting value of the static friction, so only kinetic friction will come into play....

 

in ground frame, the lower block experiences only one force i.e. kinetic frictional force which is 39.2N which creates an acceleration of 0.98 m/s² in the lower block.

 

now, in the lower block frame, the slab experiences 3 forces-> 100N towards right, kinetic frictional force (39.2N) towards left & pseudo force(9.8N) towards left. the resultant force on the slab is 51N towards right, therefore, the acceleration of the slab is 5.1m/s²