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 =2 g sin theta - f = 2a`...(2) where f= force of limiting friction `mu R = mu mg cos theta = 0.3 xx 2 g xx cos 30^@` SOLVING (1) and (2) `a = 4.87 m//s^2` `T = 24.65 N`