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

Which of the following is self adjusting in nature?

A block of mass $15 \;kg$ is placed on a long trolley. The coefficient of static friction between the block and the trolley is $0.18$. The trolley accelerates from rest with $0.5 \;m s ^{-2}$ for $20 \;s$ and then moves with uniform velocity. Discuss the motion of the block as vlewed by

$(a)$ a stationary observer on the ground,

$(b)$ an observer moving with the trolley.

A uniform chain of length $L$ which hanges partially from a table, is kept in equilibrium by friction. The maximum length that can withstand without slipping is $l$ , then coefficient of friction between the table and the chain is

A force acts on a block as shown in figure. Find time when block loses contact with surface.

A body of mass $10$ kg slides along a rough horizontal surface. The coefficient of friction is $1/\sqrt 3 $. Taking $g = 10\,m/{s^2}$, the least force which acts at an angle of $30^o $ to the horizontal is ...... $N$