Rocket engines lift a rocket from the Earth's surface because hot gases with high velocity:

1. push against the Earth.

2. push against the air.

3. react against the rocket and push it up.

4. heat up the air, which lifts the rocket.

A force of \(50\) dynes is applied to a body of mass \(5\ \text{g}\), which is at rest for an interval of \(3\) seconds; then the impulse is: 

1. \(0 .15 × 10^{-3}  \ \text{Ns}\)
2. \(0 .98 × 10^{-3}\ \text{N s}\)
3. \(1.5 × 10^{-3}\ \text{N s}\)$\mathrm{}$
4. \(2.5 × 10^{-3}\ \text{N s}\)$\mathrm{}$

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 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 \(2\ \text{kg}\) 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. \(1.25\ \text{N}\)