Two blocks of mass `m_(1)=10kg` and `m_(2)=5kg` connected to each other by a massless inextensible string of length `0.3m` are placed along a diameter of the turntable. The coefficient of friction between the table and `m_(1)` is `0.5` while there is no friction between `m_(2)` and the table. the table is rotating with an angular velocity of `10rad//s`. about a vertical axis passing through its center `O`. the masses are placed along the diameter of the table on either side of the center `O` such that the mass `m_(1)` is at a distance of `0.124m` from `O`. the masses are observed to be at a rest with respect to an observed on the tuntable `(g=9.8m//s^(2))`.
(a) Calculate the friction on `m_(1)`
(b) What should be the minimum angular speed of the turntable so that the masses will slip from this position?
(c ) How should the masses be placed with the string remaining taut so that there is no friction on `m_(1)`.

Options

A. `12.82 rad//s`
B. `10.28 rad//s`
C. `13.56 rad//s`
D. `11.67 rad//s`

Answer

D

Explanation

`f_(max)=mumg=0.5xx10xx9.8=49N`
`T+f=m_(1)r_(1)omega^(1^2)`
`m_(2)r_(2)omega^(1^2)+49=m_(1)r_(1)w^(1^2),omega^(1)=11.67 rad//sec`