Choose the incorrect alternative:

1. Newton's first law is the law of inertia.

2. Newton's first law states that if the net force on a system is zero, the acceleration of any particle of the system is not zero.

3. Action and reaction act simultaneously.

4. The area under the force-time graph is equal to the change in momentum.

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:
1.  0.99 ms^-2
2.  3 ms^-2
3.  2 ms^-2
4.  0.77 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 Ns

2. 20 Ns

3. 12Ns

4. 6 Ns

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 $\left(\hat{\mathrm{i}} + 2\hat{\mathrm{j}}\right)$ . 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 (g = 10 m/s)

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 $\overrightarrow{\mathrm{F}}=6{\mathrm{t}}^2\hat{\mathrm{i}}+4\mathrm{t}\hat{\mathrm{j}}$ is applied to the object, then the velocity of the object at t = 3 second will be :

1. $18\hat{\mathrm{i}}+3\hat{\mathrm{j}}$

2. $18\hat{\mathrm{i}}+6\hat{\mathrm{j}}$

3. $3\hat{\mathrm{i}}+18\hat{\mathrm{j}}$

4. $18\hat{\mathrm{i}}+4\hat{\mathrm{j}}$

A rigid ball of mass M strikes a rigid wall at ${60}^0$ 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:
      

1.  Mv

2.  2Mv

3.  Mv/2

4.  Mv/3