The blocks $1$ and $2$ in the arrangement have mass $m$ each. The strings $AB$ and $BC$ are light, havir $T_1$ and $T_2$ respectively. The system is in equilibrium with a constant horizontal force $mg$ acting on

The machine as shown has $2$ rods of length $1 \mathrm{m}$ connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has roller that rolls along the floor in a slot. As the roller goes back and forth, a $2 \mathrm{kg}$ weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a :

A particle moving with velocity $\overrightarrow{V}$ is acted by three forces shown by the vector triangle $PQR$. The velocity of the particle will

Four identical beakers contain same amount of water as shown below.

Beaker $A$ contains only water. A lead ball is held submerged in the beaker $B$ by string from above. A same sized plastic ball, say a table tennis $\left(TT\right)$ ball, is held submerged in beaker $C$ by a string attached to a stand from outside. Beaker $D$ contains same sized $TT$ ball which is held submerged from a string attached to the bottom of the beaker. These beakers (without stand) are placed on weighing pans and register readings $w_A, w_B, w_C$ and $w_D$ for $A, B, C$ and $D$ respectively. Effects of the mass and volume of the stand and string are to be neglected.

A block $A$ of mass $100 \mathrm{kg}$ rests on another block $B$ of mass $200 \mathrm{kg}$ and is tied to a wall as shown in the figure. The coefficient of friction between $A$ and $B$ is $0.2$ and that between $B$ and ground is $0.3$. The minimum force required to move the block $B$ is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$