If the radius of curvature of the path of two particles of same mass are in the ratio $$3: 4$$, then in order to have constant centripetal force, their velocities will be in the ratio of :

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 vehicle of mass $$200 \mathrm{~kg}$$ is moving along a levelled curved road of radius $$70 \mathrm{~m}$$ with angular velocity of $$0.2 ~\mathrm{rad} / \mathrm{s}$$. The centripetal force acting on the vehicle is:

A coin placed on a rotating table just slips when it is placed at a distance of $$1 \mathrm{~cm}$$ from the center. If the angular velocity of the table in halved, it will just slip when placed at a distance of _________ from the centre :