Three solids of masses ${m_1},\,{m_2}$ and ${m_3}$ are connected with weightless string in succession and are placed on a frictionless table. If the mass ${m_3}$ is dragged with a force T, the tension in the string between ${m_2}$ and ${m_3}$ is

A mass $M$ is placed on a very smooth wedge resting on a surface without friction. Once the mass is released, the acceleration to be given to the wedge so that $M$ remains at rest is $a$ where

Three blocks of masses $3\, kg, 2\, kg$ and $1\, kg$ are placed side by side on a smooth  surface as shown in figure. A horizontal force of $12\,N$ is applied to $3\, kg$ block. The  net force on $2\, kg$ block is ............ $N$

A block '$A$' takes $2\,s$ to slide down a frictionless incline of $30^{\circ}$ and length ' $l$ ', kept inside a lift going up with uniform velocity ' $v$ '. If the incline is changed to $45^{\circ}$, the time taken by the block, to slide down the incline, will be approximately $........\,s$

Three blocks are connected as shown in figure on a horizontal frictionless table. If $m_1 =  1kg, m_2 = 8kg, m_3 = 27\, kg$ and $T_3 = 36N, T_2$ will be ............ $N$

Two blocks $A$ and $B$ of masses $3\,m$ and $m$ respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of $A$ and $B$ immediately after the string is cut, are respectively