Question

In the arrangement shown, the pulleys are fixed and ideal, the strings are light, m₁> m₂, and S is a spring balance which is itself massless. The reading of S (in units of mass) is –

• A. m₁ – m₂
• B. $\frac { 1 } { 2 }$ (m₁ + m₂)
• C. $\frac { \mathrm { m } _ { 1 } \mathrm {~m} _ { 2 } } { \mathrm {~m} _ { 1 } + \mathrm { m } _ { 2 } }$
• D. $\frac { 2 \mathrm {~m} _ { 1 } \mathrm {~m} _ { 2 } } { \mathrm {~m} _ { 1 } + \mathrm { m } _ { 2 } }$

Answer 1

Answer: (D)

$\frac { 2 \mathrm {~m} _ { 1 } \mathrm {~m} _ { 2 } } { \mathrm {~m} _ { 1 } + \mathrm { m } _ { 2 } }$

Answer 2

Acceleration of system = $\frac { m _ { 1 } - m _ { 2 } } { m _ { 1 } + m _ { 2 } }$ g

Tension in string = $\frac { 2 \mathrm {~m} _ { 1 } \mathrm {~m} _ { 2 } } { \mathrm {~m} _ { 1 } + \mathrm { m } _ { 2 } }$ g

reading of spring balance is T.