The retarding acceleration of $7.35\, ms^{-2}$ due to frictional force stops the car of mass $400\, kg$ travelling on a road. The coefficient of friction between the tyre of the car and the road is

A block of mass $5\, kg$ is $(i)$ pushed in case $(A)$ and $(ii)$ pulled in case $(B)$, by a force $F = 20\, N$, making an angle of $30^o$ with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is $\mu = 0.2$. The difference between the accelerations of the block, in case $(B)$ and case $(A)$ will be ........ $ms^{-2}$ .$(g = 10\, ms^{-2})$

A block of mass $1\, kg$ is at rest on a horizontal table. The coefficient of static friction  between the block and the table is $0.5.$ The magnitude of the force acting upwards at  an angle of $60^o$ from the horizontal that will just start the block moving is

A block of mass $m$ is pressed against a vertical surface by a spring of unstretched length $l$ . If the coefficient of friction between the block and the surface is $\mu $. Choose the correct statement.

An isolated rail car originally moving with speed $v_0$ on a straight, frictionles, level track contains a large amount of sand. $A$ release valve on the bottom of the car malfunctions, and sand begins to pour out straight down relative to the rail car. What happens to the speed of the rail car as the sand pours out? 

A uniform rope of total length $l$ is at rest on a table with fraction $f$ of its length hanging (see figure). If the coefficient of friction between the table and the chain is $\mu$, then