Two blocks of mass 2 kg and 5 kg are connected by an ideal string passing over a pulley. The block of mass 2 kg is free to slide on a surface inclined at an angle of 30^@ with the horizontal whereas 5 kg block hangs freely. Find the acceleration of the system and the tension in the string.

Two blocks of mass 2 kg and 5 kg are connected by an ideal string pass

1.	Two blocks of mass 2 kg and 5 kg are connected by an ideal string passing over a pulley. The block of mass 2 kg is free to slide on a surface inclined at an angle of 30^@ with the horizontal whereas 5 kg block hangs freely. Find the acceleration of the system and the tension in the string.
Answer» Solution : Let a be the acceleration of the SYSTEM and T be the Tension in the string. Equations of motions for 5 kg and 2 kg blocks are 5g-T=5a .......(1) `T-2g SIN theta-f=2a ........(2)` where f=force of limitating FRICTION `=muR=u mg cos theta=0.3 xx 2g xx cos 30^(@)` Solving (1) & (2), `a=4.87 m//s^(2)` T=24.65 N