Question

Derive the expression for acceleration and tension in two bodies
connected by a string, one placed on the smooth table using free
body diagram.​

Answer 1

Given :

Two blocks are connected as shown in the figure.

To Derive :

Expression for acceleration and tension in two bodies.

Solution :

Let mass of body A be m₁, mass of body B be m₂ (m₁ > m₂) and common acceleration of the system be a$.$

A] Net force on block A :

➙ m₁g - T = m₁a .......... (I)

B] Net force on block B :

➙ T = m₂a .......... (II)

On adding both equations, we get

➛ (m₁g - T) + T = (m₁ + m₂) a

➛ m₁g = (m₁ + m₂) a

➛ a = m₁g / (m₁ + m₂)

❒ Tension force in the string :

From the second equation;

➙ T = m₂a

➙ T = m₂ × m₁g / (m₁ + m₂)

➙ T = m₁m₂g / (m₁ + m₂)