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A particle of mass \( m_{1} \) moves in a circular path of radius \( R \) on a rotating table. A string connecting the particles \( m_{1} \) and \( m_{2} \) passes over a smooth hole made on the table as shown in figure. If mass \( m_{1} \) does not slide relative to the rotating .table, mark the correct option(s) as applicable.
(1) The friction force acting on the block \( m_{1} \) is \( \left(m_{1} \omega^{2} R-m_{2} g\right) \) along radial rotation towards center of rotation.
(2) The friction force acting on the block \( m_{1} \) is \( \left(m_{1} \omega^{2} R-m_{2} g\right) \) along tangent direction in the direction opposite to \( \vec{v} \).
(3) The maximum angular velocity of the particle is \( \sqrt{\left(\frac{m_{2}+\mu m_{1}}{m_{1}}\right) \frac{g}{R}} \).
(4) The minimum angular velocity of the particle is \( \sqrt{\left(\frac{m_{2}-\mu m_{1}}{m_{1}}\right) \frac{g}{R}} \).
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