question_answer

Two masses \[{{M}_{1}}\]and \[{{M}_{2}}\] are attached to the ends of a string which passes over a pulley attached to the top of an inclined plane. The angle of inclination of the plane is, 30° and \[{{M}_{1}}=10\text{ }kg,{{M}_{2}}=5\text{ }kg.\] What is the acceleration of mass \[{{M}_{2}}\]?

A)  \[10m/{{s}^{2}}~\]                        

B) \[~5m/{{s}^{2}}\]

C)  \[\frac{2}{3}m/{{s}^{2}}\]                                           

D)  Zero

Correct Answer: D

Solution :

                The free body diagram showing the various forces acting on the system are: For \[{{M}_{1}},\] \[{{M}_{1}}g\sin \theta -T={{M}_{1}}a\]                           ?.. (i) For \[{{M}_{2}},\] \[T-{{M}_{2}}g={{M}_{2}}a\]                  ?.. (ii) Adding Eqs. (i) and (ii), we get \[{{M}_{1}}g\sin \theta -{{M}_{2}}g=({{M}_{1}}+{{M}_{2}})a\] \[\Rightarrow \]               \[a=\frac{({{M}_{1}}\sin \theta -{{M}_{2}})g}{{{M}_{1}}+{{M}_{2}}}\]                 \[=\frac{\left( 10\times \frac{1}{2}-5 \right)}{10+5}g=0\]