Each of the three blocks P, Q and R shown in the figure has a mass of 3 kg. P and Q rest on a smooth horizontal table and are joined by wire A; wire B runs from Q over a smooth pulley at the edge of the table and carries the hanging block R. Each of the wires A and B has cross-sectional area 0.005…

Question

Each of the three blocks P, Q and R shown in the figure has a mass of 3 kg. P and Q rest on a smooth horizontal table and are joined by wire A; wire B runs from Q over a smooth pulley at the edge of the table and carries the hanging block R. Each of the wires A and B has cross-sectional area 0.005 cm² and Young's modulus 2×10¹¹ N m⁻². Neglecting friction, the longitudinal strain in wire B is ×10⁻⁴. (Take g=10 m s⁻²)

Accepted Answer

2. Given: m_P=m_Q=m_R=3 kg, A=0.005 cm²=5×10⁻⁷ m², Y=2×10¹¹ N m⁻². Only R's weight drives the system while all three masses share the acceleration: a=(m_Rg)/(m_P+m_Q+m_R)=(30)/9=(10)/3 m s⁻². Wire B holds back the falling block R, so m_Rg-T_B=m_Ra, giving T_B=3(10-(10)/3)=20 N. Strain =(T_B)/(AY)=(20)/(5×10⁻⁷×2×10¹¹)=(20)/(10⁵)=2×10⁻⁴. Hence the answer is 2.

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