Physics - NLM Question with Solution | TestHub

The FBD of A, B, C are shown

$T=m{a}_1$

$2mg-2T=2m{a}_2$

$T+3mg\sin 30^{\circ }=3m{a}_3$

constraint relation:

$$a_1+a_3=2a_2$$

solving the equations

$a_1=\frac{9}{20}\mathrm{g}=4.5\mathrm{m}{\mathrm{s}}^{-2}$

$a_2=\frac{11}{20}\mathrm{g}=5.5\mathrm{m}{\mathrm{s}}^{-2}$

$a_3=\frac{13}{20}\mathrm{g}=6.5\mathrm{m}{\mathrm{s}}^{-2}$

$T=\frac{9}{20}\mathrm{mg}=4.5\mathrm{N}$

The rope tension is T = 4.5 N. The string connected to block B carries 2T = 9 N, not 4.5 N, so option D is false. Options A, B and C are correct.