Starting from rest, a body slides down a $45°$ inclined plane in twice the time it takes to slide down the same distance in the absence of friction. The coefficient of friction between the body and the inclined plane is

A wooden block of mass $m$ resting on a rough horizontal table (coefficient of friction $=\mu$) is pulled by a force $F$, as shown in the figure. The acceleration of the block moving horizontally is:

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

Two blocks, $m_1=4 \mathrm{kg}$ and $m_2=4 \mathrm{kg}$, are connected by a weightless rod on a plane having an inclination of $37°$. If the coefficient of dynamic friction of $m_1$ and $m_2$, with the inclined plane is $0.25$, then the common acceleration of the two blocks and the tension in the rod, respectively, are:

A force $F=t$ is applied to block $A$ as shown in the figure. The force is applied at $t=0$ seconds when the system was at rest and the string is just straight without tension. Which of the following graphs gives the frictional force $f$ between block $B$ and the horizontal surface as a function of time $t.$

A body of mass $10 \mathrm{kg}$ lies on a rough inclined plane of inclination $\theta ={\sin }^{-1}\left(\frac{3}{5}\right)$ with the horizontal. When a force of $30 \mathrm{N}$ is applied on the block parallel on an upward the plane, the total reaction by the plane on the block is nearly along,

Block $A$ of mass $4 \mathrm{kg}$ and block $B$ of mass $6 \mathrm{kg}$ are resting on a horizontal surface, as shown in the figure. There is no friction between the block $B$ and the horizontal surface. The coefficient of friction between the blocks is $0.2.$ If the value of $g=10 \mathrm{m} {\mathrm{s}}^{-2}$, then the maximum horizontal force $F$ that can be applied on the block $B$ without any relative motion between $A$ and $B$ is:

Two blocks $A$ and $B$ plane surface as shown in the figure. The mass of block $A$ is $100 \mathrm{kg}$ and that of block $B$ is $200 \mathrm{kg}$. Block $A$ is tied to a stand and block $B$ is pulled by a force $F.$ If the coefficient of friction between the surfaces of $A$ and $B$ is $0.2$ and the coefficient of friction between $B$ and the plane is $0.3,$ then for the motion of $B,$ the minimum value of $F$ will be: