Find the tension $T$ needed to hold the cart in equilibrium, if there is no friction.

A block of mass $5 \mathrm{k}\mathrm{g}$ is (i) pushed in case $\left(\mathrm{A}\right)$ and (ii) pulled in case $\left(\mathrm{B}\right),$ by a force $\mathrm{F}=20\mathrm{ }\mathrm{N},$ making an angle of ${30}^o$ with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is $\mu =0.2.$ The difference between the accelerations of the block, in case $\left(\mathrm{B}\right)$ and case $\left(\mathrm{A}\right)$ will be:
$\left(\mathrm{g}=10\mathrm{m}\mathrm{ }{\mathrm{s}}^{-2}\right)$

A spherical body of mass $2 \mathrm{kg}$ starting from rest acquires a kinetic energy of $10000 \mathrm{J}$ at the end of $5^{\text{th }}$ second. The force acted on the body is _____ $\mathrm{N}$.

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 $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$