If the chain is lowered at a constant speed v=1.2m/s, the normal reaction exerted on the floor as a function of time is (19.2 + 40xt) N. The chain has a mass of 80kg and a total length of 6m. The value of ‘x’ is ____. $\left[\mathrm{Take} \mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2\right]$

Net force exerted by the chain on the table is $\mathrm{F}=\mathrm{W}+{\mathrm{F}}_{\mathrm{t}}$

Where W = Weight of chain on the table in a time $\mathrm{t};{\mathrm{F}}_{\mathrm{t}}=\text{ Thrust force }$ 

Linear mass density of chain $=\frac{80}{6}=\frac{40}{3}\mathrm{kg}/\mathrm{m}$

Weight of portion of chain lying on ground = $\mathrm{mg}=\frac{40}{3}\left(1.2\mathrm{t}\right)\times 10=160\mathrm{t} \mathrm{N}$

Thrust force $=F_t=V\times \frac{dm}{dt}=\left(1.2\right)\lambda \mathrm{V}$

$=\left(1.2\right)\frac{40}{3}\left(1.2\right)=19.2\mathrm{N}$

Normal reaction exerted on floor $=(160\mathrm{t}+19.2)$

N is Vertically downward.