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

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 masses, \(A\) and \(B\), each of mass \(M\) are fixed together by a massless spring. A force acts on the mass \(B\) as shown in the figure. If the mass \(B\) starts moving away from mass \(A\) with acceleration \(a\) in the ground frame, then the acceleration of mass \(A\) will be:

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:

Three blocks \(A\), \(B\) and \(C\) of mass \(3M\), \(2M\) and \(M\) respectively are suspended vertically with the help of springs \({PQ}\) and \({TU}\) and a string \({RS}\) as shown in Figure. 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 \({RS}\) is cut will be: 
1. \(g\) downward
2. \(g\) upward
3. more than \(g\) downward
4. zero

A massless and inextensible string connects two blocks \(\mathrm{A}\) and \(\mathrm{B}\) of masses \(3m\) and \(m,\) respectively. The whole system is suspended by a massless spring, as shown in the figure. The magnitudes of acceleration of \(\mathrm{A}\) and \(\mathrm{B}\) immediately after the string is cut, are respectively:
         

Find the reading of the spring balance is shown in the figure.
(take \(g=10~\text{m/s}^2\) )
                

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

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

If the system shown in the figure is in equilibrium, then the reading of spring balance (in kgf) is:

1. \(10\)

2. \(20\)

3. \(100\)

4. zero