Masses and ( ) are arranged as follows: and are connected by a light string over a…

PHYSICS · Subjective · CBSE · Physics · Laws of Motion · Laws of Motion

Problem

Masses m1, m2m_1,\,m_2 and m3m_3 (m2>m1m_2>m_1) are arranged as follows: m1m_1 and m2m_2 are connected by a light string over a smooth pulley A. From the side of m2m_2 hangs a second light string that passes over another smooth pulley B carrying mass m3m_3 on its free end. All strings are light and inextensible, and both pulleys are ideal. (i) Derive expressions for the acceleration of each mass in terms of m1, m2, m3m_1,\,m_2,\,m_3 and gg. (ii) Hence calculate the numerical values of the accelerations and the tensions in the two string segments when m1=2 kgm_1=2\,\text{kg}, m2=3 kgm_2=3\,\text{kg} and m3=4 kgm_3=4\,\text{kg} (g=9.8 m s−2g=9.8\,\text{m\,s}^{-2}).

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