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

                           
1. \(2.5~\text{m/s}^2\)
2. \(4~\text{m/s}^2\)
3. \(5~\text{m/s}^2\)
4. zero

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

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:

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

A simple pendulum hangs from the roof of a train moving on horizontal rails. If the string is inclined towards the front of the train, then the train is:

A body of mass \(m\) is moving on a concave bridge \(ABC\) of the radius of curvature \(R\) at a speed \(v.\) The normal reaction of the bridge on the body at the instant it is at the lowest point of the bridge is:

1. \(mg-\frac{mv^{2}}{R}\)
2. \(mg+\frac{mv^{2}}{R}\)
3. \(mg\)
4. \(\frac{mv^{2}}{R}\)

The angle of banking for a cyclist taking a turn at a curve is given by \(\tan\theta   =   \frac{v^{n}}{rg}\) where symbols have their usual meaning. The value of \(n\) is: