Two masses 52 kg and 48 kg are attached to the ends of a string that passes over a frictionless pulley. Find the tension in the string and acceleration in the bodies when both the masses are moving vertically. Ans. (500 N,0.4 ms⁻²)


Given:  

Mass of the 1st body = m₁ = 52 kg
Mass of the 2nd body = m₂ = 48 kg
Gravitational Acceleration = g = 10 m s⁻²


To Find:

Tension in the string = T = ?
Acceleration in the bodies = a =   ? 



Solution:  

The formula for Tension in the string when the two bodies m₁ and m₂ attached to the end of a string passing over a frictionless pulley and moving vertically is:

T = `\ frac {2m₁m₂}{m₁ + m₂}` g

putting values 

T = `\ frac {2 ｘ 52 kg ｘ 48 kg}{52 kg + 48 kg}` ｘ 10 m s⁻²


T = `\frac{49,920}{100}` Kgms⁻²

T = 499.2 N

The formula for Acceleration in the bodies m₁ and m₂ attached to the end of a string passing over a frictionless pulley and moving vertically is


a = `\ frac {m₁ - m₂}{m₁ + m₂}` g


by putting values

a = `\ frac {52 kg - 48 kg}{52 kg + 48 kg}` ｘ 10 m s⁻²

a = `\frac{40}{100}` m s⁻²

a = 0.4 m s⁻²

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