Question

please answer this question.....

Answer 1

▶ Solution :

Given :

A system of three blocks of masses 4kg, 6kg and 12kg respectively is provided.

To Find :

Acceleration of hanging block.

Concept :

First we have to draw FBD of all three blocks. After that we can calculate tension force in the string with the help of FBD.

Diagram :

Please, see the attachment for better understanding.

Calculation :

• For first block :

▪ T = m1a1

▪ T = 4a1

• For second block :

▪ T = m2a2

▪ T = 6a2

• For third block :

▪ m3g - 2T = m3a3

▪ 12g - 2T = 12a3

▪ 6g - T = 6a3

• Constraint motion equation :

▪ a1 + a2 = 2a3

As per above equation,

$\sf\:\dfrac{T}{4}+\dfrac{T}{6}=\dfrac{6g-T}{3}\\ \\ \sf\:3T+2T=24g-4T\\ \\ \sf\:5T+4T=24g\\ \\ \bf\:T=\dfrac{24g}{9</p><p>}\\ \\ \implies\sf\:6g-T=6a_3\\ \\ \implies\sf\:6g-\dfrac{24g}{9}=6a_3\\ \\ \implies\sf\:g-\dfrac{4g}{9}=a_3\\ \\ \implies\boxed{\bf{\pink{a_3=\dfrac{5g}{9}}}}$