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 Newton’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.

Question and Answers

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. \(\begin{array}{l}\frac{Pm}{M+m}\end{array} \)
2. \(\begin{array}{l}\frac{PM}{M+m}\end{array} \)
3. \(\begin{array}{l}\frac{Pm}{M-m}\end{array} \)
4. \(\begin{array}{l}{P}\end{array} \)

Answer: (b)

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. \(\begin{array}{l}\frac{Fx}{L-x}\end{array} \)
2. \(\begin{array}{l}\frac{FL}{L-x}\end{array} \)
3. \(\begin{array}{l}\frac{F(L-x)}{L}\end{array} \)
4. \(\begin{array}{l}\frac{FL}{x}\end{array} \)

Answer: (c)

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

Answer: (a) 13 N

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

Answer: (a) 5.44 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

Answer: (a) 9 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. \(\begin{array}{l}\frac{m_2}{m_1+m_2+m_3}T\end{array} \)
2. \(\begin{array}{l}\frac{m_3}{m_1+m_2+m_3}T\end{array} \)
3. \(\begin{array}{l}\frac{m_2+m_3}{m_1+m_2+m_3}T\end{array} \)
4. \(\begin{array}{l}\frac{m_1+m_2}{m_1+m_2+m_3}T\end{array} \)

Answer: (d)

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

Answer: (c) 73.5 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

Answer: (c) g/3

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

1. \(\begin{array}{l}\frac{2}{\sqrt{3}}\end{array} \)
2. \(\begin{array}{l}\frac{\sqrt{3}}{2}\end{array} \)
3. \(\begin{array}{l}2\sqrt{3}\end{array} \)
4. \(\begin{array}{l}2\end{array} \)

Answer: (b) 

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

Answer: (c) 4 kg

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