Đáp án:

 \(12,19\left( {m/s} \right)\)

Giải thích các bước giải:

a) Ta có: 

\(\begin{array}{l}
\omega  = \dfrac{v}{l} = \dfrac{3}{{1,5}} = 2\left( {rad/s} \right)\\
{a_{ht}} = \dfrac{{{v^2}}}{l} = \dfrac{{{3^2}}}{{1,5}} = 6\left( {m/{s^2}} \right)
\end{array}\)

b) Ta có: 

\(\begin{array}{l}
T.\cos \alpha  = P \Rightarrow \cos \alpha  = \dfrac{P}{T} = \dfrac{{0,5.10}}{{50}} = \dfrac{1}{{10}}\\
 \Rightarrow \sin \alpha  = \dfrac{{3\sqrt {11} }}{{10}}\\
{F_{ht}} = T\sin \alpha  = 50.\dfrac{{3\sqrt {11} }}{{10}} = 15\sqrt {11} \left( N \right)\\
 \Rightarrow m\dfrac{{{v^2}}}{R} = 15\sqrt {11} \\
 \Rightarrow 0,5.\dfrac{{{v^2}}}{{l.\sin \alpha }} = 15\sqrt {11} \\
 \Rightarrow v = 12,19\left( {m/s} \right)
\end{array}\)