question_answer

In the given figure the pulley is assumed massless and frictionless. If the friction force on the object of mass m is \[f\], then its acceleration in terms of the force F will be equal to:            

A) \[(F-f)/m\]                        

B) \[\left( \frac{F}{2}-f \right)/m\]

C) F/m                                      

D) none of these

Correct Answer: D

Solution :

To find the acceleration of the block we will need the tension in the string, that can be obtained by considering the pulley as the system. The force acting on the pulley are (i) F towards right (ii) T towards left by the portion BC of the string and (iii) T towards left by the portion BA of the string. Since there is no vertical motion. Then vertical force if any, add to zero. As the pulley is massless, the equation of motion is                                 \[F-2T=0\]                 or                            \[T=\frac{F}{2}\] The acceleration of the block is \[a=\frac{T}{m}=\frac{F}{2m}\]