question_answer

Two blocks of mass 4 kg and 2 kg are attached by an inextensible light string as shown in figure. Both the blocks are pulled vertically upwards by a force F = 120 N. Find, (a) The acceleration of the blocks (b) Tension in the string. (Take \[\text{g}=\text{1}0\text{m/}{{\text{s}}^{\text{2}}}\]).

Answer:

(a) Let ?a? be the acceleration of the blocks and T the tension in the string as shown in figure. Taking the two blocks and the string as the system. Using\[\sum {{F}_{y}}=m{{a}_{y}}\]we get \[F-4g-2g=(4+2)a\]or \[120-40-20=6a\]or \[60=6a\] \[\therefore \,\,a=10\,\,m/{{s}^{2}}\] (b) Free body diagram of 2 kg block is as shown in figure. Using \[\sum {{F}_{y}}=m{{a}_{y}}\] we get \[T-2g=2a\,\,or\,\,T-20=(2)(10)\] \[\therefore \,\,\,T=40\,N\]