Three forces starts acting simultaneously on a particle moving with velocity $\overrightarrow{v}.$ These forces are represented in magnitude and direction by the three sides of a triangle ABC (as shown). The particle will now move with velocity 

(1) $\overrightarrow{v}$ remaining unchanged

(2) Less than $\overrightarrow{v}$

(3) Greater than $\overrightarrow{v}$

(4) $\overrightarrow{v}$ in the direction of the largest force BC

Two blocks are connected by a string as shown in the diagram. The upper block is hung by another string. A force F applied on the upper string produces an acceleration of 2 m/s² in the upward direction in both the blocks. If T and T’ be the tensions in the two parts of the string, then 

(1) T = 70.8 N and T’ = 47.2 N

(2) T = 58.8 N and T’ = 47.2 N

(3) T = 70.8 N and T’ = 58.8 N

(4) T = 70.8 N and T’ = 40.2 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) 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) $\frac{m_2+m_3}{m_1+m_2+m_3}T$