A body under the action of a force $\overrightarrow{F}=6\hat{\mathrm{i}}-8\hat{\mathrm{j}}+10\hat{\mathrm{k}}$, acquires an acceleration of $1 \mathrm{m} {\mathrm{s}}^{-2}$. The mass of this body must be

Three blocks with masses $m\text{,} 2m$ and $3m$ are connected by strings as shown in the figure. After an upward force $F$ is applied on block $m$, the masses move upward with constant speed $v$. What is the net force on the block of mass $2m$? $(g$ is the acceleration due to gravity)

Three blocks $A\text{,} B$ and $C$ of masses $4 \mathrm{kg}\text{,} 2 \mathrm{kg}$ and $1 \mathrm{kg}$, respectively, are in contact on a frictionless surface as shown. If a force of $14 \mathrm{N}$ is applied on the $4 \mathrm{kg}$ block, then the contact force between $A$ and $B$ is,

Two blocks $A$ and $B$ of masses $3m$ 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,

A block of mass $m$ is placed on a smooth inclined wedge $ABC$ of inclination $\theta$ as shown in the figure. The wedge is given an acceleration $a$ towards the right. The relation between $a$ and $\theta$ for the block to remain stationary on the wedge is,