A particle is describing circular motion in a horizontal plane in contact with the smooth inside surface of a fixed right circular cone with its axis vertical and vertex down. The height of the plane of motion above the vertex is $h$ and the semivertical angle of the cone is $\alpha $ . The period of revolution of the particle
increases as $h$ increases keeping $\alpha $ same
decreases as $h$ increases keeping $\alpha $ same
decreases as $\alpha $ increases keeping $h$ same
None of these
An aircraft executes a horizontal loop at a speed of $720\; km/h$ with its wings banked at $15^o$. What is the radius of the loop in $km$?
Obtain the formula for the maximum safe speed $(v_{max})$ of a vehicle on a level curved road.
Three identical particles are joined together by a thread as shown in figure. All the three particles are moving in a horizontal plane. If the velocity of the outermost particle is $v_0$, then the ratio of tensions in the three sections of the string is
A motorcycle is travelling on a curved track of radius $500\,m$. If the coefficient of friction between road and tyres is $0.5$, the speed avoiding skidding will be ....... $m/s$
Two bodies of equal masses revolve in circular orbits of radii ${R_1}$ and ${R_2}$ with the same period. Their centripetal forces are in the ratio