# Motion of Connected Bodies MCQ for NEET

When objects are connected by a string and a force F is applied either vertically or horizontally, it produces tension in the string which affects the acceleration up to an extent. A question involving the motion of two connected bodies can be solved using the following approach:

The basic way to solve the problem is by drawing a free body diagram. The free-body diagram represents the bodies and connectors and equates the forces using Newtonâ€™s second and third laws. Along with these equations, the extra equations that one would be needing are the equations on the constraints on the connectors. Suppose the connector is a rod, then the constraint is that the length of the rod remains constant. Likewise, various constraints are applicable to various types of connectors.

1. A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m. If P is the force exerted on the free end of the rope, what is the force exerted on the block by the rope?

1. $$\frac{Pm}{M+m}$$
2. $$\frac{PM}{M+m}$$
3. $$\frac{Pm}{M-m}$$
4. $${P}$$

Answer: (b) $$\frac{PM}{M+m}$$

2. A rope of length L is pulled by a constant force F. The tension in the rope at a distance x from the end where the force is applied is

1. $$\frac{Fx}{L-x}$$
2. $$\frac{FL}{L-x}$$
3. $$\frac{F(L-x)}{L}$$
4. $$\frac{FL}{x}$$

Answer: (c) $$\frac{F(L-x)}{L}$$

3. Three weights A, B and C of mass 2 kg each are hanging on string passing through a frictionless pulley. What is the tension in the string connecting weights B and C?

1. 13 N
2. 19.6 N
3. 3.3 N
4. 0

4. A frictionless pulley kept on a horizontal table connects two blocks of masses 4 kg and 5 kg. What is the acceleration of 5 kg mass?

1. 5.44 m/s2
2. 2.72 m/s2
3. 19.5 m/s2
4. 49 m/s2

5. Three blocks A, B and C each weighing 1, 8, and 27 kg respectively are connected to each other by an inextensible string and are moving on a smooth surface. If T3 is equal to 36 N, then what will T2 be equal to?

1. 9 N
2. 18 N
3. 3.375 N
4. 1.25 N

6. Three solid masses m1, m2 and m3 placed on a frictionless table and are connected in succession. If the mass m3 is dragged with a force T, the tension in the string between m2 and m3 are given as

1. $$\frac{m_2}{m_1+m_2+m_3}T$$
2. $$\frac{m_3}{m_1+m_2+m_3}T$$
3. $$\frac{m_2+m_3}{m_1+m_2+m_3}T$$
4. $$\frac{m_1+m_2}{m_1+m_2+m_3}T$$

Answer: (d) $$\frac{m_1+m_2}{m_1+m_2+m_3}T$$

7. A string passing over a frictionless pulley has a mass of 6 kg attached to one of its ends. To the other end a mass of 10 kg is attached. What is the tension in the thread?

1. 2.45 N
2. 24.5 N
3. 73.5 N
4. 79 N

8. What will the acceleration of the system of two masses connected to a pulley be if the masses weigh 5 kg and 10 kg?

1. g
2. g/2
3. g/3
4. g/4

9. A body of weight 2 kg is suspended as shown in the figure. What is the tension T1 in the horizontal string?

1. $$\frac{2}{\sqrt{3}}$$
2. $$\frac{\sqrt{3}}{2}$$
3. $$2\sqrt{3}$$
4. $$2$$

Answer: (b)Â $$2\sqrt{3}$$

10. A block of mass which weighs 4 kg is suspended through spring balances A and B. Then A and B will read respectively

1. 0 kg and 4 kg
2. 4 kg and 0 kg
3. 4 kg and 4 kg
4. 2 kg and 2 kg