Two bodies of mass, \(4~\text{kg}\) and \(6~\text{kg}\), are tied to the ends of a massless string. The string passes over a pulley, which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (\(g\)) is:

            

1.	\(\dfrac{g}{2}\)	2.	\(\dfrac{g}{5}\)
3.	\(\dfrac{g}{10}\)	4.	\(g\)

An object of mass \(m\) is held against a vertical wall by applying horizontal force \(F\) as shown in the figure. The minimum value of the force \(F\) will be: (Consider friction between wall and object.)
             
1. Less than \(mg\)
2. Equal to \(mg\)
3. Greater than \(mg\)
4. Cannot determine

Two masses, \(m_1\) and \(m_2\) are experiencing the same force where \(m_1<m_2\). The ratio of their acceleration \(\frac{a_{1}}{a_{2}}\) is:
1. \(1\)
2. less than \(1\)
3. greater than \(1\)
4. all the three cases

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 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. \(135^\circ\)

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

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. \(1~\text{ms}^{-2}, 96~\text{N}\)

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: