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 ${\lambda }^2$

$O$ is a point at the bottom of a rough plane inclined at an angle $\alpha$ to the horizontal. Coefficient of friction between $AB$ is $\frac{\tan \alpha }{2}$ and between $BO$ is $\frac{3 \tan \alpha }{2}.\mathrm{B}$ is the mid-point of $AO.$ A block is released from rest at $A.$ Then identify which graphs are correct during motion of block from point $A$ to $O$ taking direction down the incline plane as positive:

In given diagram what is the minimum value of a horizontal external force $F$ on Block $\text{'}A\text{'}$ so that block $\text{'}B\text{'}$ will slide on ground is:

In the given diagram what is the minimum force $\text{'}F\text{'}$ required, so that block $\text{'}A\text{'}$ will slip on block $\text{'}B\text{'}$?

With reference to the figure shown, if the coefficient of friction at the surfaces is $0.42,$ then the force required to pull out the $6.0 \mathrm{kg}$ block with an acceleration of $1.50 \mathrm{m} {\mathrm{s}}^{-2}$ will be:

Two blocks $A$ and $B$ are as shown in figure. The minimum horizontal force $F$ applied on block $\text{'}B\text{'}$ for which slipping begins at $\text{'}B\text{'}$ and ground is: