Question

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 1

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 θ – f = 2a ...(2) 

where f = force of limiting friction 

= µR = µ mg cos θ = 0·3 × 2g × cos 30° 

Solving (1) & (2), 

a = 4·87 m/s² 

T = 24·65 N.