Consider the situation shown in figure. The block `B` moves on a frictionless surface ,while the coefficient of friction between `A` and the surface on which it moves is `0.2`. Find the acceleration with which the masses move and also the tension in the strings. `(Take g = 10 m//s^(2))`.

Options

A. `T_(1) =12N`
B. `T_(1) =32N`
C. `T_(1) =22N`
D. `T_(1) =42N`

Answer

B

Explanation

Let a be the acceleration with which the masses move and `T_(1)` and `T_(2)` be the tensions in left and right strings. Friction on mass `A` is `mumg =8N`. Then equationof motion `A,B` and `C` are
For mass `A` `T_(1) -8 = 4a` …(i)
For mass `B` `T_(2) = 8a` …(ii)
For mass `C` `200-T_(1) -T_(2) = 20a` …(iii)
Adding the above three equation, we get `32a =192`
or `a = 6m//s^(2)`
From Eqs,(i) and (ii), we have `T_(2) = 48N`
and `T_(1) =32N`