Question

In the arrangement shown in Fig. pulleys are smooth and massless. Threads are massless and inextensible. Find acceleration of mass m₁.

• A. $\frac { \left[ 2 m _ { 1 } m _ { 2 } + m _ { 0 } \left( m _ { 1 } - m _ { 2 } \right) \right] g } { 2 m _ { 1 } m _ { 2 } + m _ { 0 } \left( m _ { 1 } + m _ { 2 } \right) }$
• B. $\frac { \left[ 4 m _ { 1 } m _ { 2 } + m _ { 0 } \left( m _ { 1 } - m _ { 2 } \right) \right] g } { 4 m _ { 1 } m _ { 2 } + m _ { 0 } \left( m _ { 1 } + m _ { 2 } \right) }$
• C. $\frac { \left[ 4 m _ { 1 } m _ { 2 } - m _ { 0 } \left( m _ { 1 } - m _ { 2 } \right) \right] g } { 4 m _ { 1 } m _ { 2 } + m _ { 0 } \left( m _ { 1 } + m _ { 2 } \right) }$
• D. None of these

Answer 1

Answer: (B)

$\frac { \left[ 4 m _ { 1 } m _ { 2 } + m _ { 0 } \left( m _ { 1 } - m _ { 2 } \right) \right] g } { 4 m _ { 1 } m _ { 2 } + m _ { 0 } \left( m _ { 1 } + m _ { 2 } \right) }$

Answer 2

m₁g – T = m₁a₁ [from Fig. (ii)]

m₂g – T = m₂a₂ [from Fig. (iii)]

m₀a = 2T [from Fig. (i)]

Solving we get a_{1 =} $\frac { \left[ 4 m _ { 1 } m _ { 2 } + m _ { 0 } \left( m _ { 1 } - m _ { 2 } \right) \right] g } { 4 m _ { 1 } m _ { 2 } + m _ { 0 } \left( m _ { 1 } + m _ { 2 } \right) }$