A block of mass $m$ is placed on a surface having vertical cross section given by $y=x^2 / 4$. If coefficient of friction is $0.5$ , the maximum height above the ground at which block can be placed without slipping is:

A rope of length $L$ and mass $M$ is being pulled on a rough horizontal floor by a constant horizontal force $F$ = $Mg$ . The force is acting at one end of the rope in the same direction as the length of the rope. The coefficient of kinetic friction between rope and floor is $1/2$ . Then, the tension at the midpoint of the rope is

The coefficient of static friction between a wooden block of mass $0.5\, kg$ and a vertical rough wall is $0.2$ The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall will be $N$ $\left[ g =10\, ms ^{-2}\right]$

What is the maximum value of the force $F$ such that the block shown in the arrangement, does not move ........ $N$

A force of $19.6\, N$ when applied parallel to the surface just moves a body of mass $10 \,kg$ kept on a horizontal surface. If a $5\, kg$ mass is kept on the first mass, the force applied parallel to the surface to just move the combined body is........ $N.$ 

A block of mass $m$ is in contact with the cart $C$ as shown in the figure. The coefficient of static friction between the block and the cart is $\mu .$ The acceleration $\alpha$ of the cart that will prevent the block from falling satisfies