A particle of mass m is suspended from a ceiling through a string of length L. The particle moves in a horizontal circle of radius r such that $$r = {L \over {\sqrt 2 }}$$. The speed of particle will be :

The normal reaction 'N' for a vehicle of 800 kg mass, negotiating a turn on a 30$$^\circ$$ banked road at maximum possible speed without skidding is ____________ $$\times$$ 10³ kg m/s². [Given cos30$$^\circ$$ = 0.87, $$\mu$$_s = 0.2]

A particle of mass m moves in a circular orbit under the central potential field, $$U(r) = - {C \over r}$$, where C is a positive constant. The correct radius $$-$$ velocity graph of the particle's motion is :

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)