Physics - NLM Question with Solution | TestHub

$$\begin{array}{rlrlr}& \text{ Acceleration of system }=\frac{\left({\mathrm{m}}_1-{\mathrm{m}}_2\right)\mathrm{g}\sin \theta }{{\mathrm{m}}_1+{\mathrm{m}}_2}=\frac{(2-1)(10)\left(\frac{1}{2}\right)}{2+1}=\frac{5}{3}\mathrm{m}/{\mathrm{s}}^2& \text{ Tension in the string }=\left(\frac{2{\mathrm{m}}_1{\mathrm{m}}_2}{{\mathrm{m}}_1+{\mathrm{m}}_2}\right)\mathrm{g}\sin \theta =\left(\frac{2\times 2\times 1}{2+1}\right)\left(10\times \frac{1}{2}\right)=\frac{20}{3}\mathrm{N}& \text{ Acceleration of }\mathrm{m}1\text{ w.r.t. }{\mathrm{m}}_2=2\mathrm{a}=2\times \frac{5}{3}=\frac{10}{3}\mathrm{m}/{\mathrm{s}}^2& \text{ Clamp force on the pulley }=2\mathrm{T}=2\times \frac{20}{3}=\frac{40}{3}\mathrm{N}\end{array}$$