A body of mass \(5~\text{kg}\) is acted upon by two perpendicular forces, \(8~\text N\) and \(6~\text N.\) The magnitude of the acceleration of the body is:
1. \(0.99~\text{ms}^{-2}\)
2. \(3~\text{ms}^{-2}\)
3. \(2~\text{ms}^{-2}\)
4. \(0.77~\text{ms}^{-2}\)

A mass \(m\) is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when:

A point mass \(m\) is moved in a vertical circle of radius \(r\) with the help of a string. The velocity of the mass is \(\sqrt{7 g r} \) at the lowest point. The tension in the string at the lowest point will be: 
1. \(6mg\)
2. \(7mg\)
3. \(8mg\)
4. \(mg\)

A string tied on a roof bears a maximum tension of \(50\) kg-wt. The minimum acceleration that can be acquired by a man of \(98\) kg to descend will be: (take \(g=9.8\) m/s²)
1. \(9.8\) m/s²
2. \(4.9\) m/s²
3. \(4.8\) m/s²
4. \(5\) m/s²

As shown in the figure, two masses of \(10~\text{kg}\) and \(20~\text{kg}\), respectively are connected by a massless spring. A force of \(200~\text{N}\) acts on the \(20~\text{kg}\) mass. At the instant shown, the \(10~\text{kg}\) mass has an acceleration of \(12~\text{m/s}^2\) towards the right. The acceleration of \(20~\text{kg}\) mass at this instant is:
          
1. \(12~\text{m/s}^2\)
2. \(4~\text{m/s}^2\)
3. \(10~\text{m/s}^2\)
4. zero

Two masses \(8~\text{kg}\) and \(12~\text{kg}\) are connected at the two ends of a light inextensible string that goes over a frictionless pulley. The acceleration of the masses and the tension in the string when the masses are released are:
1. \(2~\text{ms}^{-2}, 69~\text{N}\)
2. \(1~\text{ms}^{-2}, 69~\text{N}\)
3. \(2~\text{ms}^{-2}, 96~\text{N}\)
4. \(1~\text{ms}^{-2}, 96~\text{N}\)

Three blocks each of mass \(m\) are hanged vertically with the help of inextensible strings and ideal springs. Initially, the system was in equilibrium. If at any instant, the lowermost string is cut, then the acceleration of the block \(B\) just after cutting the string will be:
   
1. \(g\)

2. \(\dfrac g 2\)

3. \(\dfrac {2g}{ 3}\)

4. zero

The angle between the position vector and the acceleration vector of a particle in a non-uniform circular motion (centre of the circle is taken as the origin) will be:
1. \(0^\circ\)
2. \(45^\circ\)
3. \(75^\circ\)
4. \(135^\circ\)

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. \(mg\sin\theta- \frac{mv^2}{R}\)