Choose the incorrect alternative:

If two forces ($6\hat{\mathrm{i}}$ $+$ $8\hat{\mathrm{j}}$) and ($4\hat{\mathrm{i}}$ $+$ $4\hat{\mathrm{j}}$) N are acting on a body of mass 2 kg, then the acceleration produced in the body in $\mathrm{m}/{\mathrm{s}}^2$ will be:

1. ($5\hat{\mathrm{i}}$ $+$ $6\hat{\mathrm{j}}$)

2. ($10\hat{\mathrm{i}}$ $+$ $12\hat{\mathrm{j}}$)

3. ($6\hat{\mathrm{i}}$ $+$ $12\hat{\mathrm{j}}$)

4. ($2\hat{\mathrm{i}}$ $+$ $3\hat{\mathrm{j}}$)

A body of mass 5 kg is acted upon by two perpendicular forces, 8 N and 6 N. The magnitude of the acceleration of the body is:

The force \(\mathrm{F}\) acting on a particle of mass \(\mathrm{m}\) 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:
        

On the application of an impulsive force, a sphere of mass \(500\) g 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, ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$ are experiencing the same force where ${\mathrm{m}}_1$< ${\mathrm{m}}_2$ . The ratio of their acceleration $\frac{{\mathrm{a}}_1}{{\mathrm{a}}_2}$ is:
1. 1
2. less than 1
3. greater than 1
4. all the three cases

An impulse of 6m$\hat{\mathrm{j}}$ 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. $-\hat{\mathrm{i}}$ $+$ $8\hat{\mathrm{j}}$

2.  $\hat{\mathrm{i}}$ $-$ $8\hat{\mathrm{j}}$

3. $\hat{\mathrm{i}}$ $+$ $8\hat{\mathrm{j}}$

4.  $8\hat{\mathrm{i}}$ $-$ $\hat{\mathrm{j}}$

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 \(\overset{\rightarrow}{F} = 6 t^{2} \hat{i} + 4 t \hat{j}\) 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: