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A horizontal force $12 \,N$ pushes a block weighing $1/2\, kg$ against a vertical wall. The coefficient of static friction between the wall and the block is $0.5$ and the coefficient of kinetic friction is $0.35.$ Assuming that the block is not moving initially. Which one of the following choices is correct (Take $g = 10 \,m/s^2$)

Block moves vertically downwards
Block moves vertically upwards
Block will not move and force exerted on the block by the wall is $12\,N$
Block will not move and force exerted on the block by the wall is $13\, N$
Solution

$\mathrm{N}=\mathrm{F}=12 \mathrm{N}$
Static frictional force $=\mu N=0.5 \times 12=6 \mathrm{N}$
$\mathrm{mg}=5 \mathrm{N}$
so friction $=\mathrm{F}_{s}=5 \mathrm{N}$
$\mathrm{F}_{\mathrm{Net}}=\sqrt{5^{2}+12^{2}}=13 \mathrm{N}$