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 block \(B\) of mass \(3\) kg is kept on block \(A\) of mass \(5\) kg in a lift accelerating upward with an acceleration of \(g.\) The reaction by \(A\) on \(B\) is:

                                                      

If the force acting on a system is zero, the quantity which remains constant is:

Two blocks, \(A\) and \(B\), of masses \(2m\) and \(4m\) are connected by a string. The block of mass \(4m\) is connected by a spring (massless). The string is suddenly cut. The ratio of the magnitudes of accelerations of masses \(2m\) and \(4m\) at that instant will be:

The reading of spring balance in the depicted figure will be:

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 \(100\) kg gun fires a ball of \(1\) kg horizontally from a cliff at a height of \(500\) m. It falls on the ground at a distance of \(400\) m from the bottom of the cliff. The recoil velocity of the gun is: (Take \(g=10\) m/s²)
1. \(0.2\) m/s
2. \(0.4\) m/s
3. \(0.6\) m/s
4. \(0.8\) m/s

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?
   $\mathrm{}$

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