A monkey of mass 50   kg climbs on a rope which can withstand the tension T of 350   N . If monkey…

Let $a_1$ be the acceleration of monkey while moving down.

F.B.D of monkey while moving downward

Using Newton's second law of motion,

$mg-T=m{a}_1$

$\therefore 500-T=50\times 4\Rightarrow T=300 \mathrm{N}$

Let $a_2$ be the acceleration of monkey while moving up.

F.B.D of monkey while moving up

Using Newton's second law of motion

$T-mg=m{a}_2$

$\Rightarrow T-500=50\times 5$

$\Rightarrow T=750 \mathrm{N}$

Breaking strength of rope $=750-300=350 \mathrm{N}$

$\therefore$$$ Rope will break while monkey is moving upward.