A modern grand-prix racing car of mass $m$ is travelling on a flat track in a circular arc of radius $R$ with a speed $v$. If the coefficient of static friction between the tyres and the track is $\mu_{s},$ then the magnitude of negative lift $F_{L}$ acting downwards on the car is
(Assume forces on the four tyres are identical and $g =$ acceleration due to gravity)
$m \left(\frac{ v ^{2}}{\mu_{ s } R }+ g \right)$
$m \left(\frac{ v ^{2}}{\mu_{ s } R }- g \right)$
$m \left( g -\frac{ v ^{2}}{\mu_{ s } R }\right)$
$-m\left(g+\frac{v^{2}}{\mu_{s} R}\right)$
A train is moving with a speed of $12 \mathrm{~m} / \mathrm{s}$ on rails which are $1.5 \mathrm{~m}$ apart. To negotiate a curve radius $400 \mathrm{~m}$, the height by which the outer rail should be raised with respect to the inner rail is (Given, $g=$ $10 \mathrm{~m} / \mathrm{s}^2$ ) :
A motorcyclist of mass m is to negotiate a curve of radius r with a speed v. The minimum value of the coefficient of friction so that this negotiation may take place safely, is
A point mass $m$ is suspended from a light thread of length $l$, fixed at $O$, is whirled in a horizontal circle at constant speed as shown. From your point of view, stationary with respect to the mass, the forces on the mass are
A car sometimes overturns while taking a turn. When it overturns, it is
A mass of $100\, gm$ is tied to one end of a string $2 \,m$ long. The body is revolving in a horizontal circle making a maximum of $200$ revolutions per min. The other end of the string is fixed at the centre of the circle of revolution. The maximum tension that the string can bear is .......... $N$. (approximately)