Question

A light string passing over a smooth light fixed pulley connects two blocks of masses \(m_1\) and \(m_2\). If the acceleration of the system is \(\frac {g}{8}\), then the ratio of masses is 

(1) \(\frac {9}{7}\)

(2) \(\frac {8}{1}\)

(3) \(\frac {4}{3}\)

(4) \(\frac {5}{3}\)

Answer 1

Correct option is (1) \(\frac {9}{7}\)

\(a =\frac {(m_1 -m_2)}{(m_1+m_2)}=\frac {g}{8}\)

\(8m_1 -8m_2 = m_1 +m_2\)

\(7m_1 = 9m_2\)

\(\frac {m_1}{m_2}=\frac {9}{7}\)