$A$ boy on a cycle pedals around a circle of $20\, m$ radius at a speed of $20\, m/s$. The combined mass of the boy and the cycle is $90\, kg$. The angle that the cycle makes with the vertical so that it may not fall is ......... $^o$ $(g = 9.8\, m/s^2)$.

$A$ small disc is placed on the top of a smooth hemisphere of radius $R$. The smallest horizontal velocity $V$ that should be imparted to the disc so that it leaves the hemisphere surface immediately is (there is no friction):

When helical gear $M$ turns as shown,gears $I$ & $H$ turn in the following manner. Which of the following is correct? (Assuming no slipping anywhere)

$A$ cyclist taking a turn bends inwards while a car passenger taking the same turn is thrown outwards. The reason is:

Two particles of the same mass are moving in circular orbits because of a force given by $F(r) = -\frac{16}{r} - r^3$. The first particle is at a distance $r = 1$,and the second is at $r = 4$. The best estimate for the ratio of kinetic energies of the first and the second particle is closest to:

$A$ particle moves in a circular orbit under the action of a central attractive force inversely proportional to the distance $r$. The speed of the particle is