A box of mass $m\, kg$ is placed on the rear side of an open truck accelerating at $4\, m/s^2$. The coefficient of friction between the box and the surface below it is $0.4$. The net acceleration of the box with respect to the truck is zero. The value of $m$ is :- $[g = 10\,m/s^2]$

- A
$4 \,kg$

- B
$8 \,kg$

- C
$9.78 \,kg$

- D
It could be any value

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

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

- [KVPY 2017]

$Assertion$ : On a rainy day it is difficult to drive a car or bus at high speed.

$Reason$ : The value of coefficient of friction is lowered due to wetting of the surface

- [AIIMS 1999]

A block of mass $5\, kg$ is on a rough horizontal surface and is at rest. Now a force of $24\, N $is imparted to it with negligible impulse. If the coefficient of kinetic friction is $0.4$ and $g = 9.8\,m/{s^2}$, then the acceleration of the block is ........ $m/s^2$

A block is moving on an inclined plane making an angle $45^{\circ}$ with the horizontal and the coefficient of friction is $\mu$. The force required to just push it up the inclined plane is $3$ times the force required to just prevent it from sliding down. If we define $N=10 \ \mu$, then $N$ is

- [IIT 2011]