A hemisphere of mass $3 \mathrm{m}$ and radius $R$ is free to slide with its base on a smooth horizontal table. A particle of mass $m$ is placed on the top of the hemisphere. If the particle is displaced with a negligible velocity, then find the angular velocity of the particle relative to the centre of the hemisphere at an angular displacement $\mathrm{\theta },$ when the velocity of the hemisphere is $v$.

A block of mass $m$ is held fixed against a wall by applying a horizontal force $F$. Which one of the following options is incorrect.

A block of mass $10 \mathrm{kg}$is suspended through two light spring balances as shown in the figure.

Two masses $A$ and $B$ of $10 \mathrm{kg}$, respectively, are connected with a string passing over a frictionless pulley fixed at the corner of a table, as shown in the figure. The coefficient of static friction of $A$ with the table is $0.2$. The minimum mass of $C$, that may be placed on $A$, to prevent it from moving, is

A block of mass $2 \mathrm{kg}$ is given a push for a moment, horizontally and then the block starts sliding over a horizontal plane. The graph shows the velocity versus time graph of the motion. The coefficient of sliding friction between the plane and the block is

The time when the relative motion between the blocks will stop is