If \(\mu\) between block \(A\) and inclined plane is \(0.5\) and that between block \(B\) and the inclined plane is \(0.8\), then the normal reaction between blocks \(A\) and \(B\) will be:
                     
1. \(180\) N
2. \(216\) N
3. \(0\)
4. None of these

Three blocks \(A\), \(B\) and \(C\) of mass \(3M\), \(2M\) and \(M\) respectively are suspended vertically with the help of springs \(\mathrm{PQ}\) and \(\mathrm{TU}\) and a string \(\mathrm{RS}\) as shown in fig. The acceleration of blocks \(A\), \(B\) and \(C\) are \(a_{1} , a_{2}~ \text{and}~ a_{3}\) respectively.
     

The value of acceleration \(a_{1}\) at the moment string \(\mathrm{RS}\) is cut will be: 
1. \(g\) downward
2. \(g\) upward
3. more than \(g\) downward
4. zero

Calculate the reading of the spring balance shown in the figure: (take \(g=10\) m/s²)
                

1. \(60\) N
2. \(40\) N
3. \(50\) N
4. \(80\) N

A metal sphere is suspended from a wall by a string. The forces acting on the sphere are shown in the figure. Which of the following statements is NOT correct?
   $\mathrm{}$

A particle of mass \(m\) having speed \(v\) goes in a vertical circular motion such that its centre is at its origin, as shown in the figure. If at any instant the angle made by the string with a negative \(y\text-\)axis is \(\theta\) then the tension in the string is:
[Take radius = \(R\)]

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

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:

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. \(\frac{mv^{2}}{R}\)

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:

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

Choose the incorrect alternative: