Physics - NLM Question with Solution | TestHub

Let T be the tension in rope A. The painter-plus-platform is held up by two strands of rope A: the strand attached to the platform and the strand the painter pulls on, so the total upward force is 2T.

Rope B supports the ceiling pulley, which carries two strands of rope A, so its tension is

$${\mathrm{T}}_{\mathrm{B}}=2\mathrm{T}$$

(C) At rest: 2T = 200 N, so T = 100 N. Correct.

$$2\mathrm{T}=200\Rightarrow \mathrm{T}=100\mathrm{N}$$

(A) Rope B can withstand at most 300 N, so 2T $\le$ 300 N. Newton's second law for painter + platform (mass = 200/10 = 20 kg):

$$2\mathrm{T}-200=20\mathrm{a}$$

$$300-200=20{\mathrm{a}}_{\max }$$

$${\mathrm{a}}_{\max }=5\mathrm{m}/{\mathrm{s}}^2$$

Correct.

(B) To hoist himself up quasi-statically rope B only needs T_B = 2T = 200 N, not 400 N. Wrong.

(D) Going downwards slowly (constant velocity) still needs 2T = 200 N, i.e. the painter pulls with only 100 N, not 200 N. Wrong.

Correct options: (A), (C).