question_answer

A block of mass 10 kg resting on a horizontal surface is connected by a cord passing over a light frictionless pulley to a hanging block of mass 10 kg as shown in the figure. The coefficient of friction between the block and the surface is 0.5. The acceleration of the system is \[\left( \text{g }==\text{ 1}0\text{ m}/{{\text{s}}^{\text{2}}} \right)\]

A) \[\text{2}.\text{5 m}/{{\text{s}}^{\text{2}}}\]                     

B)  \[0.\text{25 m}/{{\text{s}}^{\text{2}}}\]

C) \[\text{5 m}/{{\text{s}}^{\text{2}}}\]             

D)         \[0.\text{5 m}/{{\text{s}}^{\text{2}}}\]

Correct Answer: A

Solution :

For block\[A,\,\,T-f=ma\] \[\Rightarrow \]   \[T-\mu mg=10a\] \[\Rightarrow \]   \[T-0.5\times 10\times 10=10\,\,a\] \[\Rightarrow \]   \[T-50=10\,\,a\]                          ? (i) For block\[B\],             \[10g-T=10a\]             \[100-T=10a\]                            ? (ii) Solving equations (i) and (ii), we get Acceleration, \[a=2.5\,\,m/{{s}^{2}}\]