A car is moving on a horizontal circular road of radius $0.1 \,km$ with constant speed. If coefficient of friction between tyres of car and road is $0.4$, then speed of car may be ......... $m / s$ $\left(g=10 \,m / s ^2\right)$
$5$
$10$
$20$
All of these
A car of mass $1000\, kg$ negotiates a banked curve of radius $90\, m$ on a frictionless road. If the banking angle is $45^o $, the speed of the car is ....... $ms^{-1}$
A stone of mass of $16\, kg$ is attached to a string $144 \,m$ long and is whirled in a horizontal circle. The maximum tension the string can withstand is $16$ Newton. The maximum velocity of revolution that can be given to the stone without breaking it, will be ....... $ms^{-1}$
If the radius of curvature of the path of two particles of same masses are in the ratio $1 : 2$, then in order to have constant centripetal force, their velocity, should be in the ratio of
Concretemixture is made by mixing cement, stone and sand in a rotating cylindrical drum . If the drum rotates too fast, the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take place. The maximum rotational speed of the drum in revolutions per minute (rpm) to ensure proper mixing is close to (Take the radius of the drum to be $1.25\, m$ and its axle to be horizontal)
A stone of mass $0.25\; kg$ tied to the end of a string is whirled round in a circle of radius $1.5 \;m$ with a speed of $40\; rev./min$ in a hortzontal plane. What is the tenston in the string? What is the maximum speed in $m/s $ with which the stone can be whirled around if the string can withstand a maximum tension of $200\; N ?$