Calculate the acceleration of mass $12 \mathrm{kg}$ and the tension in the string connecting to $12 \mathrm{kg}$ mass, shown in the figure (the strings are weightless and inextensible; the pulleys are weightless and frictionless).

Take acceleration due to gravity as $g$.

Two blocks are in contact on a frictionless table. One is of mass $m$ and the other of mass $2m$. A force $F$ is applied on $2m$ as shown in the figure. Now, the same force $F$ is applied from the right on $m$. In the two cases, respectively, the ratio of forces of contact between the two blocks will be

Two forces of $6 \mathrm{N}$ and $3 \mathrm{N}$ are acting on the two blocks of $2 \mathrm{kg}$ and $1 \mathrm{kg}$ kept on a frictionless floor, respectively. What is the force exerted on the $2 \mathrm{kg}$ block by the $1 \mathrm{kg}$ block?

A $50 \mathrm{kg}$ homogeneous smooth sphere rests on $30°$ incline $A$ and bears against the smooth vertical wall $B$. The contact forces at $A$ and $B$, respectively, are (assume $g=10 \mathrm{m} {\mathrm{s}}^{-2}$).

Two smooth spheres $A$ and $B$ each of radius $5 \mathrm{cm}$ and weight $W$ rest on one another inside a fixed smooth cylinder of radius $8 \mathrm{cm}$. The reactions between the spheres and the vertical side of the cylinder, respectively, are

A cylinder of mass $M$ and radius $R$ is resting on two corner edges $A$ and $B$ as shown in the figure. The normal reaction at the edges $A$ and $B$, respectively, are (neglect friction)

In all the given cases, blocks are at rest and in contact. The forces applied are as shown. All the surfaces are smooth. Then, in which of the following cases normal reaction the two blocks is zero?