Two masses 26 kg and 24 kg are attached to the ends of a string which passes over a frictionless pulley. 26 kg mass is lying over a smooth horizontal table. 24 N mass is moving vertically downward. Find the tension in the string and the acceleration in the bodies. Ans. (125 N, 4.8 ms⁻²)


Given:  

Mass of the 1st body moving vertically = m = 24 kg
Mass of the 2nd body moving horizontally along the table= m = 26 kg
Gravitational Acceleration = g = 10 m s⁻²

To Find:

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

Solution:  

Formula for Tension in the string when the one body is moving vertically and the 2nd body moves horizontally

T = `\ frac {m₁m₂}{m₁ + m₂}` g

putting values 

T = `\ frac {24 kg x 26 kg}{24 kg + 26 kg}` x 10 m s⁻²

T = `\frac{6240kg²}{50kg}` m s⁻²

T = 124.8 kg m s⁻² 

T ≈ 125 N

Formula for acceleration in the bodies when one body is moving vertically and the 2nd body moves horizontally

a = `\ frac {m₁}{m₁ + m₂}` g

by putting values

a = `\ frac {24 kg}{24 kg + 26 kg}` x 10 m s⁻²

a = `\frac{240 kg}{50 kg}` m s⁻²

a = 4.8 m s⁻²

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