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

A body is moving with a velocity of 2$\hat{\mathrm{i}}$ m/s. If the force acting on the body is \((2\hat i+3\hat j+3\hat k)\) N, then the momentum of the body is changing in:

1. X-direction only

2. X-Y directions

3. Y-Z directions

4. In all X-Y-Z directions

A parachutist falls downward with an acceleration of \(2\) $\mathrm{m}/{\mathrm{s}}^2$ at a height of \(200\) m from the ground. Calculate the upthrust of air if the mass of the parachutist is \(60\) kg (assume g = 10 $\mathrm{m}/{\mathrm{s}}^2$)

1. \(480\) N

2. \(620\) N

3. \(720\) N

4. \(600\) N

What is the minimum value of force F such that at least one block leaves the ground in the given figure? (g = 10 $\mathrm{m}/{\mathrm{s}}^2$)

1. 20 N, 2 kg leaves the ground first

2. 30 N, 3 kg leaves the ground first

3. 40 N, 2 kg leaves the ground first

4. 50 N, 3 kg leaves the ground first

The block of mass m (shown in the figure) does not move on applying the inclined force F. The friction force acting on the block is:

Fundamentally, the normal force between two surfaces in contact is:

1. Electromagnetic

2. Gravitational

3. Weak nuclear force

4. Strong nuclear force

A particle of mass m is suspended from a ceiling through a massless string. The particle moves in a horizontal circle as shown in the given figure. The tension in the string is:
 

1. mg

2. 2mg

3. 3mg

4. 4mg

A particle of mass m is attached to a string and is moving in a vertical circle. Tension in the string when the particle is at its highest and lowest point is ${\mathrm{T}}_1$ $\mathrm{and}$ ${\mathrm{T}}_2$ respectively. Here $\left({\mathrm{T}}_2\right)$ $-$ ${\mathrm{T}}_1$ is equal to: