A monkey of mass 50kg climbs on a rope which can withstand the...

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,

$mg - T = m{a}_{1}$

$∴ 500 - T = 50 \times 4 ⇒ T = 300N$

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

$T - mg = m{a}_{2}$

$⇒ T - 500 = 50 \times 5$

$⇒ T = 750N$

Breaking strength of rope $= 750 - 300 = 350N$

$∴$ Rope will break while monkey is moving upward.