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A block of mass m(1)=2 kg is kept on a s...

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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