A coin placed on a rotating table just slips when it is placed at a distance of $1\,cm$ from the center. If the angular velocity of the table in halved, it will just slip when placed at a distance of from the centre $............\,cm$

A car is moving with uniform velocity on a rough horizontal road. Therefore, according to Newton's first law of motion

Calculate the maximum acceleration (in $m s ^{-2}$) of a moving car so that a body lying on the floor of the car remains stationary. The coefficient of static friction between the body and the floor is $0.15$ $\left( g =10 m s ^{-2}\right)$.

A force $f$ is acting on a block of mass $m$. Coefficient of friction between block and surface is  $\mu$. The block can be pulled along the surface if :-

A particle of mass $m$ is at rest at the origin at time $t = 0$. It is subjected to a force $F(t) = F_0e^{-bt}$ in the $x$ -direction. Its speed $v(t)$ is depicted by which of  the  following curves ?

A $2\,kg$ block slides on a horizontal floor with a speed of $4\, m/s$. It strikes a  uncompressed spring, and compresses it till the block is motionless. The kinetic friction  force is $110\,N$ and spring constant is $1000\, N/m$. The spring compresses by ........ $cm$