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

 

1.	\(20~\text{N}, 2~\text{kg}\) leaves the ground first.
2.	\(30~\text{N}, 3~\text{kg}\) leaves the ground first.
3.	\(40~\text{N}, 2~\text{kg}\) leaves the ground first.
4.	\(50~\text{N}, 3~\text{kg}\) 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:

                       
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. \(4mg\)

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 \(T_1\) $\mathrm{and}$ \(T_2\) respectively. Here \(T_2-T_1\) is equal to: 

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 \(K = aS^2\) 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. \(\tan^{-1}\left(\frac{S}{R}\right)\)
2. \(\tan^{-1}\left(\frac{R}{S}\right)\)
3. \(\tan^{-1}\left(\frac{a}{R}\right)\)
4. \(\tan^{-1}\left(\frac{R}{a}\right)\)

The tension in the string connecting blocks, \(B\) and \(C\), placed on a smooth horizontal surface in the following diagram is:

If two forces \(\left(6 \hat{i}+8\hat j\right)\) and \(\left(4 \hat{i}+4\hat j \right)\)N are acting on a body of mass \(2\) kg, then the acceleration produced in the body (in \(\text{m/s}^{2}\)) will be:
1. \(\left(5 \hat{i}+6\hat j\right)\)
2. \(\left(10 \hat{i}+12\hat j\right)\)
3. \(\left(6 \hat{i}+12\hat j\right)\)
4. \(\left(2 \hat{i}+3\hat j\right)\)