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?

                                    

1.	\(0.5X\)	2.	\(3X\)
3.	\(2X\)	4.	\(X\)

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. \(\frac{F \left(M + 2 m\right)}{m + M}\)
2. \(F \over {m +M}\)
3. \(\frac{FM}{m}\)
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 \(6m \hat{j}\) 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. \(4mg\)