Two blocks each of mass $m$ are placed on a rough horizontal surface and connected by a massless inelastic string as shown. The coefficient of friction between each block and horizontal surface is $\mu .$ The string connecting both the blocks initially has zero tension. The minimum force to be applied on block $A$ to just move the two block system horizontally (without the string getting slack) is :

A mass $m$ is supported as shown in the figure by ideal strings connected to a rigid wall and to a mass $3m$ at rest on a fixed horizontal surface. The string connected to larger mass is horizontal, that connected to smaller mass is vertical and the one connected to wall makes an angle $60°$ with horizontal.Then the minimum coefficient of static friction between the larger mass and the horizontal surface that permits the system to remain in equilibrium in the situation shown is:

The coefficient of friction between the block $A$ of mass $m$ and block $B$ of mass $2\mathrm{m}$ is $\mu .$ There is no friction between block $B$ and the inclined plane. If the system of blocks $A$ and $B$ are released from rest and there is no slipping between $A$ and $B,$ then

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