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

A balloon with mass 'm' is descending down with an acceleration 'a' (where a < g). How much mass should be removed from it so that it starts moving up with an acceleration 'a'?

1. $\frac{2ma}{g+a}$

2. $\frac{2ma}{g-a}$

3. $\frac{ma}{g+a}$

4. $\frac{ma}{g-a}$

A body of mass (4m) is lying in the x-y plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass (m) move perpendicular to each other with equal speeds (u). The total kinetic energy generated due to explosion is:

1. $m{u}^2$

2. 1.5$m{u}^2$

3. 2$m{u}^2$

4. 3$m{u}^2$

The upper half of an inclined plane of inclination θ is perfectly smooth while the lower half is rough. A block starting from rest at the top of the plane will again come to rest at the  bottom if the coefficient of friction between the block and the lower half of the plane is given by:

1. μ = 2/tanθ
2. μ = 2tanθ
3. μ = tanθ
4. μ = 1/tanθ

Three blocks with masses m, 2m, and 3m are connected by strings as shown in the figure. After an upward force F is applied on block m, the masses move upward at constant speed v. What is the net force on the block of mass 2m? (g is the acceleration due to gravity). 

        

1. 2mg
2. 3mg
3. 6mg
4. zero

A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45^o, the speed of the car is:

1. 20 ms^-1

2. 30 ms^-1

3. 5 ms^-1

4. 10 ms^-1

A body of mass M hits normally a rigid wall with velocity v and bounces back with the same velocity. The impulse experienced by the body is:

1.  1.5Mv

2.  2Mv

3.  zero

4.  Mv

A block of mass m is in contact with the cart C as shown in the figure. 
        
The coefficient of static friction between the block and the cart is $\mathrm{\mu }$. The acceleration $\mathrm{\alpha }$ of the cart that will prevent the block from falling satisfies:

1. $\mathrm{\alpha }>\frac{\mathrm{mg}}{\mathrm{\mu }}$

2. $\mathrm{\alpha }>\frac{\mathrm{g}}{\mathrm{\mu m}}$

3. $\mathrm{\alpha }\ge \frac{\mathrm{g}}{\mathrm{\mu }}$

4. $\mathrm{\alpha }<\frac{\mathrm{g}}{\mathrm{\mu }}$