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

Three identical masses, each of mass 4 kg, are connected by massless inextensible strings. The string joining A and B passes over a massless frictionless pulley as shown in the figure. The tension in the string connecting mass B and C is:

1. 40 N

2. 20 N

3. 26.67 N

4. 13.33 N

Two masses, A and B, of mass 4 kg and 1 kg, respectively, are connected with the help of a massless inextensible string. Mass A is placed on a rough horizontal table, and mass B is suspended with the help of a string passing through a smooth hole at the centre of the table. For the system to be in equilibrium, what should be the minimum value of the coefficient of friction?

1. 0.5

2. 0.25

3. 2.5

4. 0.125

What is the acceleration of block A, if the acceleration of B is 4 $\mathrm{m}/{\mathrm{s}}^2$ towards the right at the instant shown?

                          
1. \(2.5~m/s^2\)
2. \(4~m/s^2\)
3. \(5~m/s^2\)
4. Zero

A 10 kg block is kept on a horizontal turntable that rotates at an angular velocity of 2 rad/s. If the distance of the block from the center of the table is 0.5 m, the net force on the block is:

1. 40 N

2. 20 N

3. 10 N

4. Zero

Two blocks of masses 2 kg and 3 kg placed on a horizontal surface are connected by a massless string. If 3 kg is pulled by 10 N as shown in the figure, then the force of friction acting on the 2 kg block will be: [Take g = 10 $\mathrm{m}/{\mathrm{s}}^2$]

Two plates of the same mass are attached rigidly to the two ends of a spring. One of the plates rests on a horizontal surface, and the other results in compression X of the spring when it is in steady-state. If an external force is applied to the upper plate to just lift off the lowest plate, what further compression in the spring is required?

Two masses, M and m, are connected by a weightless string. They are pulled by a force on a frictionless horizontal surface. The tension in the string will be:

1.  $\frac{\mathrm{F}\left(\mathrm{M}+2m\right)}{\mathrm{m}+\mathrm{M}}$

2. \(F \over {m +M}\)

3.  $\frac{\mathrm{FM}}{\mathrm{m}}$

4.  \(Fm \over {m + M}\)

If the system shown in the figure is in equilibrium, then the reading of spring balance (in kgf) is:

1. 10

2. 20

3. 100

4. Zero

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