An impulse of \(6m \hat{j}\) 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. \(-\hat i + 8\hat j\)
2. \(\hat i - 8\hat j\)
3. \(\hat i + 8\hat j\)
4. \(8\hat i - \hat j\)

A body is moving with a velocity of \(2\hat i\) 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. \(X\text-Y\) directions
3. \(Y\text-Z\) directions
4. In all \(X\text-Y\text-Z\) directions

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

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:

                       
1. \(F \cos\theta\)
2. \(F \sin\theta\)
3. \(\mu mg-F \sin\theta\)
4. \(\mu mg\)

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. \(4mg\)

Choose the incorrect alternative:

A block slides down on a \(45^{\circ}\) rough incline in thrice the time it takes to slide down on a frictionless \(45^{\circ}\) incline of the same length. The coefficient of friction between the block and the rough incline is:

The kinetic energy 'K' of a particle moving in a circular path varies with the distance covered S as K = a${\mathrm{S}}^2$, where a is constant. The angle between the tangential force and the net force acting on the particle is: (R is the radius of the circular path)

1.  ${\tan }^{-1}\left(\frac{\mathrm{S}}{\mathrm{R}}\right)$

2.  ${\tan }^{-1}\left(\frac{\mathrm{R}}{\mathrm{S}}\right)$

3.  ${\tan }^{-1}\left(\frac{\mathrm{a}}{\mathrm{R}}\right)$

4.  ${\tan }^{-1}\left(\frac{\mathrm{R}}{\mathrm{a}}\right)$