A car of $800 \mathrm{~kg}$ is taking turn on a banked road of radius $300 \mathrm{~m}$ and angle of banking $30^{\circ}$. If coefficient of static friction is $0.2$ then the maximum speed with which car can negotiate the turn safely : $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \sqrt{3}=1.73\right)$

The maximum speed that can be achieved without skidding by a car on a circular unbanked road of radius $R$ and coefficient of static friction $\mu $, is

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 $200\; N ?$

The normal reaction $'{N}^{\prime}$ for a vehicle of $800\, {kg}$ mass, negotiating a turn on a $30^{\circ}$ banked road at maximum possible speed without skidding is $...\,\times 10^{3}\, {kg} {m} / {s}^{2}$ [Given $\left.\cos 30^{\circ}=0.87, \mu_{{s}}=0.2\right]$

A cyclist turns around a curve at $15\, miles/hour$. If he turns at double the speed, the tendency to overturn is

A car of mass $1000\,kg$ negotiates a banked curve of radius $90\,m$ on a frictionless road. If banking angle is $45^o$ , the maximum speed of car is ............ $m/s$     $[g = 10\,m/s^2]$