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 start acting simultaneously on a particle moving with velocity \(\vec v\). 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. \(\vec v\) remaining unchanged
2. Less than \(\vec v\)
3. Greater than \(\vec v\)
4. \(\vec v\) 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 in the upward direction in both the blocks. If \(T\) and \(T’\) be the tensions in the two parts of the string, then:

1. \(T = 70.8\ \text{N}\ \text{and}\ T’ = 47.2\ \text{N}\)
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 \(2\ \text{kg}\) 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