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) gtanα

(3) g/tanα

(4) gcosecα

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) $\frac{Pm}{M+m}$

(3) $\frac{PM}{M+m}$

(4) $\frac{Pm}{M-m}$

Three equal weights A, B and C of mass 2 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 N

(3) 3.3 N

(4) 19.6 N

Two masses of 4 kg and 5 kg are connected by a string passing through a frictionless pulley and are kept on a frictionless table as shown in the figure. The acceleration of 5 kg mass is

(1) 49 m/s²

(2) 5.44 m/s²

(3) 19.5 m/s²

(4) 2.72 m/s²

Two masses 2 kg and 3 kg are attached to the end of the string passed over a pulley fixed at the top. The tension and acceleration are

(1) $\frac{7g}{8};\frac{g}{8}$

(2) $\frac{21g}{8};\frac{g}{8}$

(3) $\frac{21g}{8};\frac{g}{5}$

(4) $\frac{12g}{5};\frac{g}{5}$

Three blocks A, B and C weighing 1, 8 and 27 kg respectively are connected as shown in the figure with an inextensible string and are moving on a smooth surface. T₃ is equal to 36 N. Then T₂ is 

(1) 18 N

(2) 9 N

(3) 3.375 N

(4) 1.25 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