In which of the following cases will a force not be required to keep the particle in the given motion?
(A) The particle is going in a circle.
(B) The particle is moving in uniform straight-line motion.
(C) The momentum of the particle is constant.
(D) The acceleration of the particle is constant.

Choose the correct option from the given ones:
1. (A) and (B)
2. (A) and (D)
3. (B) and (C)
4. (C) and (D)

A ball of mass \(150\ \text{g}\) starts moving with an acceleration of \(20\ \text{m/s}^2\) when hit by a force, which acts on it for \(0.1\ \text{s}\). The impulsive imparted is:

1. \(0.5\ \text{N-s}\)
2. \(0.1\ \text{N-s}\)
3. \(0.3\ \text{N-s}\)
4. \(1.2\ \text{N-s}\)

A body of constant mass has constant linear momentum. Which of the following quantities must remain constant? 

1. force.

2. velocity.

3. acceleration.

4. All of these

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

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 \(5\ \text{g}\), initially at rest. If it 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. \(2.5 × 10^{-3}\ \text{N s}\)$\mathrm{}$

A bullet of mass \(0.1\ \text{kg}\) is fired with a speed of \(100\ \text{m/s}\), the mass of the gun is \(50\ \text{kg}\). The velocity of recoil is:

1. \(0.2\ \text{m/s}\)
2. \(0.1\ \text{m/s}\)
3. \(0.5\ \text{m/s}\)
4. \(0.05\ \text{m/s}\)

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. \(\dfrac {Pm}{M-m}\)$\frac{}{}$