In the pulley system, the mass of ball is 1.2 times greater than the mass of the rod. The length of the rod is 50 ~cm . The ball is set on the same level as the lower end of the rod and then released. What is the acceleration of the rod with which it comes down? Assume the pulleys and threads are massless and friction force is neglected. (Use, g=10 ~m / s ^2 )

Step-by-step solution

The free body diagram for given system is as shown below For ball, m a₁=2 T-m g For rod, M a₂=M g-T As, thread is uniform and of constant length, so 2 a₁=a₂ From Eq. (i), we get m a₂ 2 =2 T-m g Multiplying Eq. (ii) by 2 and adding to Eq. (iii), we get gathered 2 M a₂+ m a₂ 2 =2 M g-m g a₂= (2 M-m) (2 M+ m 2 ) g= (2- m M ) (2+ m 2 M ) g gathered Here, m M =1.2 and g=10 ~ms ⁻² aligned a₂ & = (2-1.2) (2+ 1.2 2 ) 10 & = 0.8 26 10= 40 1.3 =3 ~m / s ^2 aligned