question_answer

A block of mass 2 kg is placed on the surface of a trolley of mass 20 kg which is on a smooth surface. The coefficient of friction between the block and the surface of the trolley is 0.25. If a horizontal force of 2 N acts on the block, the acceleration of the system in \[m{{s}^{-2}}\]is \[(g=10m{{s}^{-2}})\]

A)  1.8                                        

B)  1.0

C)  0.9                                        

D)  0.09

Correct Answer: D

Solution :

                 The force of limiting friction between the  block and trolley \[{{f}_{L}}=\mu R=\mu mg\] \[=0.25\times 2\times 10=5N\] Since,                    \[F=2N,F<{{f}_{L}}\] So, both will move together with acceleration \[{{a}_{B}}={{a}_{r}}=\frac{2}{20+2}=\frac{1}{11}=0.09m/{{s}^{2}}\]