A force of 50 dynes is acted on a body of mass 5 g which is at rest for an interval of 3 seconds, then impulse is 

1. $0.15\times {10}^{-3}Ns$

2. $0.98\times {10}^{-3}Ns$

3. $1.5\times {10}^{-3}Ns$

4. $2.5\times {10}^{-3}Ns$

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. \(\dfrac {Pm}{M+m}\)

3. \(\dfrac {PM}{M+m}\)

4. \(\dfrac {Pm}{M-m}\)$\frac{}{}$

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