A block of mass $M = 5\,kg$ is resting on a rough horizontal surface for which the coefficient of friction is $0.2$. When a force $F = 40\,\,N$ is applied, the acceleration of the block will be  ........ $m/\sec^2$ $(g = 10\,\,m/{\sec^2})$

Given below are two statements:

$Statement$ $(I)$ : The limiting force of static friction depends on the area of contact and independent of materials.

$Statement$ $(II)$ : The limiting force of kinetic friction is independent of the area of contact and depends on materials.

In the light of the above statements, choose the most appropriate answer from the options given below:

A body of mass $10\,kg$ is moving with an initial speed of $20\,m / s$. The body stops after $5\,s$ due to friction between body and the floor. The value of the coefficient of friction is (Take acceleration due to gravity $g =10\; ms ^{-2}$)

An insect crawls up a hemispherical surface very slowly. The coefficient of friction between the insect and the surface is $1/3$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha $ with the vertical, the maximum possible value of $\alpha $ so that the insect does not slip is given by

A particle is moving along the circle $x^2 + y^2 = a^2$ in anti clock wise direction. The $x-y$ plane is a rough horizontal stationary surface. At the point $(a\, cos\theta , a\, sin\theta )$, the unit vector in the direction of friction on the particle is:

A particle is projected with a speed ${v_0} = \sqrt {gR} $ . The coefficient of friction between the particle and the hemispherical plane is $\mu  = 0.5$ . Then, the initial acceleration of the particle is