A heavy body of mass $25\, kg$ is to be dragged along a horizontal plane $\left( {\mu = \frac{1}{{\sqrt 3 }}} \right).$ The least force required is ........ $kgf$
$25$
$2.5$
$12.5$
$6.25$
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 $0.15$ $\left( g =10 m s ^{-2}\right)$.
Aball of mass $m$ is thrown vertically upwards.Assume the force of air resistance has magnitude proportional to the velocity, and direction opposite to the velocity's. At the highest point, the ball's acceleration is
A circular racetrack of radius $300\; m$ is banked at an angle of $15^o$. If the coefficient of friction between the wheels of a race-car and the road is $0.2$, what is the
$(a)$ optimum speed of the racecar to avoid wear and tear on its tyres, and
$(b)$ maximum permissible speed to avoid slipping ?
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 :-