Two blocks of masses $\mathrm{m}$ and $2\mathrm{m}$ are placed one over the other as shown in the figure. The coefficient of friction between $\mathrm{m}$ and $2\mathrm{m}$ is $\mathrm{\mu }$ and between $2\mathrm{m}$ and ground is $\frac{\mathrm{\mu }}{3}$. If a horizontal force $\mathrm{F}$ is applied on the upper block and $\mathrm{T}$ is the tension developed in the string, then choose the incorrect alternative.

Two blocks ($m=0.5 \mathrm{kg}$ and $M=4.5 \mathrm{kg}$) are arranged on a horizontal frictionless table as shown in the figure. The coefficient of static friction between the two blocks is $\frac{3}{7}.$ Then the maximum horizontal force that can be applied on the larger block so that the blocks move together is $N.$ (Round off to the Nearest Integer) [Take $g$ as $9.8 \mathrm{m} {\mathrm{s}}^{-2}$]

A system of two blocks of masses $m=2 \mathrm{kg}$ and $M=8 \mathrm{kg}$ is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is $0.5$. The maximum horizontal force $F$ that can be applied to the block of mass $M$ so that the blocks move together will be $\left(g=9.8 \mathrm{m} {\mathrm{s}}^{-2}\right)$

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 block of mass $5 \mathrm{kg}$ resting on a horizontal surface is connected by a cord, passing over a light frictionless pulley to a hanging block of mass $5 \mathrm{kg}$. The coefficient of kinetic friction between the block and the surface is $0.5$. Tension in the cord is $\left(g=9.8 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A block of mass $5 \mathrm{kg}$ is kept against an accelerating wedge with a wedge angle of $45°$ to the horizontal. The co-efficient of friction between the block and the wedge is $\mu =0.4$. What is the minimum absolute value of the acceleration of the wedge to keep the block steady. Assume $g=10 \mathrm{m} {\mathrm{s}}^{-2}$