Three blocks \(A\), \(B\) and \(C\) each of mass \(2\ \text{kg}\) each are hanging on a string passing over a fixed frictionless pulley as shown in the figure. The tension in the string connecting weights  \(B\) and \(C\) is:

1. Zero
2. \(13\ \text{N}\)
3. \(3.3\ \text{N}\)
4. \(19.6\ \text{N}\)

Two masses of \(4\ \text{kg}\ \text{and}\ 5\ \text{kg}\) are connected by a light and inextensible string passing over a massless and frictionless pulley and are kept on a frictionless table as shown in the figure. The acceleration of \(5\ \text{kg}\) mass is:

1. \(49\ \text{m/s}^2\)
2. \(5.44\ \text{m/s}^2\)
3. \(19.5\ \text{m/s}^2\)
4. \(2.72\ \text{m/s}^2\)

Two masses \(2\ \text{kg}\) and \(3\ \text{kg}\) are attached to the end of the string passed over a pulley fixed at the top. The tension and acceleration are:

1. \(\dfrac{7g}{8}\ ;\ \dfrac{g}{8}\)
2. \(\dfrac{21g}{8}\ ;\ \dfrac{g}{8}\)
3. \(\dfrac{21g}{8}\ ;\ \dfrac{g}{5}\)
4. \(\dfrac{12g}{5}\ ;\ \dfrac{g}{5}\)

Three blocks \(A,\ B\) and \(C\), having masses of \(1,\ 8\) and \(27\ \text{kg}\) respectively, are connected as shown in the figure with an inextensible string and are moving on a smooth surface. \(T_3\) is equal to \(36\ \text{N}\). Then \(T_2\) is:

1. \(18\ \text{N}\)
2. \(9\ \text{N}\)
3. \(3.375\ \text{N}\)
4. \(1.25\ \text{N}\)

Two bodies of mass 3 kg and 4 kg are suspended at the ends of massless string passing over a frictionless pulley. The acceleration of the system is (g = 9.8 m/s²) 

1. 4.9 m/s²

2. 2.45 m/s²

3. 1.4 m/s²

4. 9.5 m/s²

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

1. $\frac{m_2}{m_1+m_2+m_3}T$

2. $\frac{m_3}{m_1+m_2+m_3}T$

3. $\frac{m_1+m_2}{m_1+m_2+m_3}T$

4. $\frac{m_2+m_3}{m_1+m_2+m_3}T$

Three blocks of masses m₁, m₂ and m₃ are connected by massless strings as shown on a frictionless table. They are pulled with a force T₃ = 40 N. If m₁ = 10 kg, m₂ = 6 kg and m₃ 4 kg, the tension T₂ will be 

1. 20 N

2. 40 N

3. 10 N

4. 32 N

A light string passes over a frictionless pulley. To one of its ends a mass of 6 kg is attached. To its other end a mass of 10 kg is attached. The tension in the thread will be 

1. 24.5 N

2. 2.45 N

3. 79 N

4. 73.5 N

Two masses of 5kg and 10kg are connected to a pulley as shown. What will be the acceleration of the system (g = acceleration due to gravity)

1. g

2. $\frac{g}{2}$

3. $\frac{g}{3}$

4. $\frac{g}{4}$

A block A of mass 7 kg is placed on a frictionless table. A thread tied to it passes over a frictionless pulley and carries a body B of mass 3 kg at the other end. The acceleration of the system is (given g = 10 ms^–2) 

1. 100 ms^–2

2. 3 ms^–2

3. 10 ms^–2

4. 30 ms^–2