Two blocks of masses \(2\ \text{kg}\) and \(4\ \text{kg}\) are connected vertically by a light, inextensible string, as shown in the figure. The upper block is pulled upward by another string, causing both blocks to accelerate upward at \(2\ \text{m/s}^2\). If  \(T\) and \(T’\)  are the tensions in the upper and lower strings, respectively, the values of  \(T\) and \(T’\)  are:

                   

1. \(T = 70.8\ \text{N}\ \text{and}\ T’ = 47.2\ \text{N}\)
2. \(T = 58.8\ \text{N}\ \text{and}\ T’ = 47.2\ \text{N}\)
3. \(T = 70.8\ \text{N}\ \text{and}\ T’ = 58.8\ \text{N}\)
4. \(T = 70.8\ \text{N}\ \text{and}\ T’ = 40.2\ \text{N}\)

A block is kept on a frictionless inclined surface with an angle of inclination \(α\). The incline is given an acceleration \(a\) to keep the block stationary. Then \(a\) is equal to:

1. \(g\)
2. \(g\tanα\)
3. \(\dfrac g{\tanα}\)
4. \(g\ \text{cosec}\ α\)

A block of mass \(M\) is pulled along a horizontal frictionless surface by a rope of mass \(m\). If a force \(P\) is applied at the free end of the rope, the force exerted by the rope on the block will be: 

1. \(P\)

2. \(\dfrac {Pm}{M+m}\)

3. \(\dfrac {PM}{M+m}\)

4. \(\dfrac {Pm}{M-m}\)$\frac{}{}$

Three blocks \(A\), \(B\) and \(C\) each of mass \(2\ \text{kg}\), 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 opposite ends of a 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