The minimum force required to start pushing a body up a rough (frictional coefficient $\mu$ ) inclined plane is $F_1$ while the minimum force needed to prevent it from sliding down, is $F_2.$ If the inclined plane makes an angle $\theta$ with the horizontal such that $\tan \theta =2\mu$, then the ratio $\frac{F_1}{F_2}$ is

Given in the figure are two blocks $A$ and $B$ of weight $20 \mathrm{N}$ and$100 \mathrm{N}$, respectively. These are being pressed against a wall by a force $F$ as shown. If the coefficient of friction between the blocks is $0.1$ and between the block $B$ and the wall is$0.15$, the frictional force applied by the wall on the block $B$ is:

Two masses $m_1=5 \mathrm{kg}$ and $m_2=10 \mathrm{kg}$ connected by an inextensible string over a frictionless pulley are moving as shown in the figure. The coefficient of friction of horizontal surface is $0.15$. The minimum weight $m$ that should be put on top of $m_2$ to stop the motion is,

A block of mass $10 \mathrm{kg}$ is kept on a rough inclined plane as shown in the figure. A force of $3 \mathrm{N}$ is applied on the block. The coefficient of static friction between the plane and the block is $0.6$. What should be the minimum value of force $P$ such that the block does not move downward? (Take, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.)

A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force $2 \mathrm{N}$ down the inclined plane. The maximum external force up the inclined plane that does not move the block is $10 \mathrm{N}$. The coefficient of static friction between the block and the plane is (take, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$),

Starting from rest, a flat car is given a constant acceleration, $a_{\mathrm{o}}=2 \mathrm{m} {\mathrm{s}}^{-2}$. A cable is connected to a crate $A$ of mass $50 \mathrm{kg}$ as shown. Neglect the friction between the floor and car wheels and mass of pulley. Calculate the corresponding tension in the cable. The coefficient of friction between crate and floor of the car is $\mu =0.3$. The tension in cable is,

The coefficient of friction between $4 \mathrm{kg}$ and $5 \mathrm{kg}$ blocks is $0.2$ and between $5 \mathrm{kg}$ block and ground is $0.1$, respectively. Choose the correct statements.