**Solving problems in mechanics: **

**Use of free-body diagram**

When a number of bodies are connected together by strings, rods, etc, it is convenient to consider each body separately and to write equation of motion for each body by taking into account all the forces acting on it and then equating the net force acting on the body to its mass times the acceleration produced.

A diagram for each body of the system showing all the forces exerted on the body by the remaining parts of the system is called free-body diagram.

The equations of motion obtained for different bodies can be solved to determine unknown quantities.

Here we are providing problems based on Motion of Connected Bodies (solution using free body diagram)

**Concepts Used**

1. When a number of bodies are connected together by strings, rods, etc., it is convenient to draw a free body diagram for each body separately by showing all the forces acting on it.

2. Equation of motion for each body is written by equating the net force acting on the body to its mass times the acceleration produced.

### Numerical Problems Based on Class 11 Physics Free Body Diagram

Q.1. In the Atwood’s machine, the system starts from rest. What is the speed and distance moved by each mass at t =3s? (Ans. 2.67 ms^{-1},4 m)

**Show Answer**

Answer: 2.67 kg ms^{-1}, 4 m

Q.2. Two bodies whose masses are = 50 kg and m2 = 150 kg are tied by a light string and are placed on a frictionless horizontal surface. When is pulled by a force F, and acceleration of 5 ms^{-2} is produced in both the bodies. Calculate the value of F. What is the tension in the string?

**Show Answer**

Answer: 1000 N, 750 N
Q.3. Three identical blocks, each having a mass m are pushed by a force F on a frictionless table as shown in Fig. 5.57. What is the acceleration of the blocks?

What is the net force on the block A? What force does A apply on B? What force does B apply on C? Show action-reaction pairs on the contact surfaces of the blocks.

**Show Answer**

Answer: F/3 m, F/3, 2F/3, F/3
Q.4. Two masses m_{1} and m_{2} are connected by a massless string as shown in Fig. 5.55. Find the value of tension in the string if a force of 200 N is applied on (i) m_{1} and (ii) m_{2}.

**Show Answer**

Answer: (i) 75 N (ii) 125 N
Q.5. In Fig., find the acceleration a of the system and the tensions T_{1} and T_{2} in the strings. Assume that

the table and the pulleys are frictionless and the strings are massless. Take g = 9.8 ms^{-2}.

**Show Answer**

Answer: 1.4 ms^{-2}, 22.4 N, 33.6 N