A block of mass `m_(1)=2` kg is kept on a smooth horizontal table. Another block of mass `m_(2)=1` kg is connected to `m_(1)` by a light inextensible string passing over a smooth pulley as shown in the figure. If the blocks are released, what will be the (a) acceleration of each block (b) tension in the string?
Text Solution
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From the F.B.D. of `m_(1)` `N=m_(1)g " " ...(1)` `T=m_(1)a " " ...(2)` From the F.B.D. of `m_(2)` `m_(2)g-T=m_(2)a " " ...(3)` (a) From (2) and (3), `m_(2)g=(m_(1)+m_(2))a` `therefore a=(m_(2))/(m_(1)+m_(2))g " " ...(4)` `=(1)/(3) xx 9.8 m//s^(2)=3.26 m//s^(2)` (b) From (2) and (4), `T=m_(1)a=(m_(1) m_(2))/(m_(1)+m_(2)) g = (2xx1)/(2+1)xx9.8N=6.52N`.
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