In the following figure (i) and (ii), all the surface are smooth string is massless and pulley is ideal. The mass of the rope is m and `T_(1)` and `T_(2)` are the Tensions in the mid points of the ropes in figure (i) and figure (ii) respectively, then `T_(1) : T_(2)` is

Options

A. `m : M`
B. `M : (M + m)`
C. `(M + m) : m`
D. `1 : 1`

Answer

B

Explanation

`T = ma`
`Mg - T = Ma`
`:. Mg = (M + m)a`
`:. a = (mg)/((M + m))`
`:. T_(1) = (m)/(2) xx (M)/((M + m)) xx g`
Now `a_(2) = (M)/(m) g`
`:. T_(2) = (m)/(2) xx (M)/(m) g`
`:. T_(1) : T_(2) = (1)/((M + m)) : (1)/(m)`
`= m : (M + m)`