Choose the incorrect alternative:

If two forces \(\left(6 \hat{i}+8\hat j\right)\) and \(\left(4 \hat{i}+4\hat j \right)\)N are acting on a body of mass \(2\) kg, then the acceleration produced in the body (in \(\text{m/s}^{2}\)) will be:
1. \(\left(5 \hat{i}+6\hat j\right)\)
2. \(\left(10 \hat{i}+12\hat j\right)\)
3. \(\left(6 \hat{i}+12\hat j\right)\)
4. \(\left(2 \hat{i}+3\hat j\right)\)

A body of mass \(5~\text{kg}\) is acted upon by two perpendicular forces, \(8~\text N\) and \(6~\text N.\) The magnitude of the acceleration of the body is:
1. \(0.99~\text{ms}^{-2}\)
2. \(3~\text{ms}^{-2}\)
3. \(2~\text{ms}^{-2}\)
4. \(0.77~\text{ms}^{-2}\)

The force \(F\) acting on a particle of mass \(m\) is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from \(0\) to \(8\) s is:

1. \(24~\text{N-s}\)
2. \(20~\text{N-s}\)
3. \(12~\text{N-s}\)
4. \(6~\text{N-s}\)

On the application of an impulsive force, a sphere of mass \(500\) grams starts moving with an acceleration of \(10\) m/s². The force acts on it for \(0.5\) s. The gain in the momentum of the sphere will be:
1. \(2.5\) kg-m/s
2. \(5\) kg-m/s
3. \(0.05\) kg-m/s
4. \(25\) kg-m/s

Two masses, \(m_1\) and \(m_2\) are experiencing the same force where \(m_1<m_2\). The ratio of their acceleration \(\frac{a_{1}}{a_{2}}\) is:
1. \(1\)
2. less than \(1\)
3. greater than \(1\)
4. all the three cases

An impulse of \(6m \hat{j}\) is applied to a body of mass m moving with velocity \(\hat i+2\hat j\). The final velocity of the body will be:
1. \(-\hat i + 8\hat j\)
2. \(\hat i - 8\hat j\)
3. \(\hat i + 8\hat j\)
4. \(8\hat i - \hat j\)

A \(100\) kg gun fires a ball of \(1\) kg horizontally from a cliff at a height of \(500\) m. It falls on the ground at a distance of \(400\) m from the bottom of the cliff. The recoil velocity of the gun is: (Take \(g=10\) m/s²)
1. \(0.2\) m/s
2. \(0.4\) m/s
3. \(0.6\) m/s
4. \(0.8\) m/s

An object of mass \(3\) kg is at rest. Now if a force of \(\overrightarrow{F} = 6 t^{2} \hat{i} + 4 t \hat{j}\) is applied to the object, then the velocity of the object at \(t =3\) second will be:
1. \(18 \hat{i} + 3 \hat{j}\)

2. \(18 \hat{i} + 6 \hat{j}\)

3. \(3 \hat{i} + 18 \hat{j}\)

4. \(18 \hat{i} + 4 \hat{j}\)

A rigid ball of mass \(M\) strikes a rigid wall at \(60^{\circ}\) and gets reflected without loss of speed, as shown in the figure. The value of the impulse imparted by the wall on the ball will be: