question_answer

Two blocks of masses \[{{\operatorname{m}}_{1}}\,=\,\,1\,kg\,\,and\,\,{{m}_{2}}=2\,kg\] are connected by massless string and placed on a horizontal frictionless surface as shown in figure. A force \[\operatorname{F} =\,\,12\,N\] is applied to mass \[{{m}_{1}}\] as shown. The acceleration of the system is

A)  \[12\,m/{{s}^{2}}\]                

B)  \[8\,m/{{s}^{2}}\]

C)  \[4\,m/{{s}^{2}}\]                  

D)  \[2\,\,m/{{s}^{2}}\]

Correct Answer: C

Solution :

We can consider \[{{m}_{1}}\,\,and\,\,{{m}_{2}}\] as a combined system. \[F=({{m}_{1}}+{{m}_{2}})a\] \[12=\left( 1+2 \right)a\] \[\operatorname{a}=4m/{{s}^{2}}\]