A $200 \mathrm{gm}$ block is pressed with a minimum force against a rough vertical wall so that the block does not fall. If coefficient of static friction between the wall $\&$ the block is $0.4.$ Find the minimum force (in Newton) $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

Value of $\mathrm{\theta }$ is increased gradually from $\mathrm{\theta }=0.$ At $\mathrm{\theta }={\tan }^{-1}\left(\frac{1}{2}\right)$ both the blocks just start slipping. Than value of ${\mu }_2$ is: $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

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-time graph of the motion. The co-efficient of sliding friction between the plane and the block is:

Four blocks are arranged on a smooth fixed horizontal surface as shown. The masses of upper blocks are $m \mathrm{kg}$ and lower blocks are $M \mathrm{kg}$ as shown in the figure. The coefficient of friction between upper and lower blocks is $\mu .$ Both the upper blocks are connected by inextensible light string having initial zero tension. For all four blocks to move with the same acceleration, the maximum value of horizontal force $F$ applied to right bottom block (as shown) is

Consider the following statements:
$\left(1\right)$ Static friction may do positive work on an object.
$\left(2\right)$ It may be possible that, on a body, kinetic friction act in the direction of motion of the body
$\left(3\right)$ A lift going down with retardation increases the weight of an object measured by a spring balance

The correct order of True/False of the above statements is:

A block is placed on a rough horizontal plane attached with an elastic spring as shown in figure.

Initially spring is unstretched. If the plane is now slowly lifted from $\mathrm{\theta }=0°$ to $\mathrm{\theta }=90°,$ then the graph showing extension in the spring $\left(x\right)$ versus angle $\left(\mathrm{\theta }\right)$ is

A block of mass m rests on a rough horrizontal surface, having friction co-efficient $\mu =0.8.$ A force $F$ is applied on the block at an angle $53°$ to the horizontal. What should be the minimum value of $F\mathit{,}$ so that the block starts sliding ?

For the arrangement shown in figure a force $F$is applied on block $A$ in horizontal direction as shown in figure so that it's acceleration is $8 \mathrm{m} {\mathrm{s}}^{-2}$  What is the acceleration of block $B$ with respect to block $A$. (Friction coefficient is$0.5$ at all surfaces and take $\left.g=10 \mathrm{m} {\mathrm{s}}^{-2}, \tan 37°=\frac{3}{4}\right)$

A small block is projected up from the bottom of a fixed incline, inclined at $60°$ from the horizontal. Coefficient of friction between the block $\&$ the incline is $\frac{\sqrt{3}}{2}$. If the ratio of descending time to ascending time is $\lambda$ then the value of ${\lambda }^2$