question_answer

A block of mass \[{{m}_{A}}=4\,\,kg\] is kept over another block of mass \[{{m}_{B}}=8\,kg\] which is kept on a smooth horizontal surface. The coefficient of friction between the blocks is 0.4. A time varying horizontal force \[F=4t\] is applied at \[t=0\] on 4 kg mass. Then the acceleration time graph of the masses A and B is \[(g=10\,m/{{s}^{2}})\]

 

A)         

B)

C)         

D)  

Correct Answer: D

Solution :

\[{{a}_{A}}={{a}_{B}}\]

\[\Rightarrow \] \[\frac{{{F}_{\min }}-0.4\times 40}{4}=\frac{16}{8}\]

\[\Rightarrow \] \[{{F}_{\min }}=24=4{{t}_{0}}\]

\[\Rightarrow \] \[{{t}_{0}}=6s\]

\[{{a}_{A}}={{a}_{B}}=\frac{F}{12}=\frac{t}{3}\]     for        \[0<t<6\,s\]

\[{{a}_{B}}=\max =2\,m/{{s}^{2}}\] for        \[t>6\,s\]

\[{{a}_{A}}=\frac{4t-16}{4}=t-4\]        for        \[t>6\,s\]