Consider a particle is moving with a minimum speed $v$ at highest point of vertical circle of radius $R$. If the radius of the circle doubled the corresponding minimum speed will be

Assume proton is rotating along a circular path of radius 1 m under a centrifugal force of $4 \times 10^{-12} \mathrm{~N}$. If the mass of proton is $1.6 \times 10^{-27} \mathrm{~kg}$, then its angular velocity of rotation is

A circular freeway entrance and exit are commonly banked to control a moving car at $14 \mathrm{~m} / \mathrm{s}$. To design similar ramp for $28 \mathrm{~m} / \mathrm{s}$ one should

A cyclist leans with the horizontal at angle $30^{\circ}$, while negotiating round a circular road of radius $20 \sqrt{3} \mathrm{~m}$. The speed of the cycle should be