Question

A pulley is attached to one arm of a balance and a string passed round it carries two masses m₁ and m₂. The balance is counter poised and the pulley is clamped so that m₁ and m₂ do not move. How much counter weight is to be reduced or increased to restore balance if the clamp is released ?

• A. $\frac { g \left( m _ { 1 } - m _ { 2 } \right) ^ { 2 } } { \left( m _ { 1 } + m _ { 2 } \right) }$ to be reduced
• B. $\frac { g \left( m _ { 1 } - m _ { 2 } \right) ^ { 2 } } { \left( m _ { 1 } + m _ { 2 } \right) }$ to be increased
• C. $\frac { g \left( m _ { 1 } - m _ { 2 } \right) } { \left( m _ { 1 } + m _ { 2 } \right) }$ to be reduced
• D. $\frac { g \left( m _ { 1 } - m _ { 2 } \right) } { \left( m _ { 1 } + m _ { 2 } \right) }$ to be increased

Answer 1

Answer: (A)

$\frac { g \left( m _ { 1 } - m _ { 2 } \right) ^ { 2 } } { \left( m _ { 1 } + m _ { 2 } \right) }$ to be reduced

Answer 2

When pulley is clamped (or masses are stationary)

W₁ = (m₁ + m₂)g ....(i)

When clamp is removed,

W₂ = 2T = $\frac { 4 \mathrm {~m} _ { 1 } \mathrm {~m} _ { 2 } } { \mathrm {~m} _ { 1 } + \mathrm { m } _ { 2 } } \mathrm {~g}$ ....(ii)

\ DW = W₁ – W₂ = $\frac { \left( m _ { 1 } - m _ { 2 } \right) ^ { 2 } } { m _ { 1 } + m _ { 2 } } \mathrm {~g}$