A loop-the-loop cart runs down an incline into a vertical circular track of radius 3 m and then describes a complete circle. Find the minimum height above the top of the circular track from which the cart must be released.
Q 60.10
Download our app for free and get startedPlay store

Image
art

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Similar Questions

  • 1
    Two discs of moments of inertia $\mathrm{I}_1$ and $\mathrm{I}_2$ about their transverse symmetry axes, respectively rotating with angular velocities to $\omega_1$ and $\omega_2$, are brought into contact with their rotation axes coincident. Find the angular velocity of the composite disc.
    View Solution
  • 2
    Using the energy conservation, derive the expressions for the minimum speeds at different locations along a vertical circular motion controlled by gravity. Is zero speed possible at the uppermost point? Under what condition/s? Also prove that the difference between the extreme tensions (or normal forces) depends only upon the weight of the object.
    View Solution
  • 3
    A solid sphere of radius $R$, rotating with an angular velocity $\omega$ about its diameter, suddenly stops rotating and $75 \%$ of its $\mathrm{KE}$ is converted into heat. If $\mathrm{c}$ is the specific heat capacity of the material in SI units, show that the temperature of $3 \mathrm{R}^2 \mathrm{CO}^2$ the sphere rises by $\frac{3 R^2 \omega^2}{20 c}$.
    View Solution
  • 4
    Do we need a banked road for a two wheeler? Explain.
    View Solution
  • 5
    On what factors does the frequency of a conical pendulum depend? Is it independent of some factors?
    View Solution
  • 6
    The radius of gyration of a body about an axis at $6 \mathrm{~cm}$ from its centre of mass is $10 \mathrm{~cm}$. Find its radius of gyration about a parallel axis through its centre of mass.
    View Solution
  • 7
    State an expression for the moment of inertia of a thin ring about its transverse symmetry axis.
    View Solution
  • 8
    A string of length $0.5 \mathrm{~m}$ carries a bob of mass $0.1 \mathrm{~kg}$ at its end. If this is to be used as a conical pendulum of period $0.4 \pi \mathrm{s}$, calculate the angle of inclination of the string with the vertical and the tension in the string.
    View Solution
  • 9
    A wheel of moment of inertia $1 \mathrm{~kg} \cdot \mathrm{m}^2$ is rotating at a speed of $40 \mathrm{rad} / \mathrm{s}$. Due to the friction on the axis, the wheel comes to rest in 10 minutes. Calculate the angular momentum of the wheel, two minutes before it comes to rest.
    View Solution
  • 10
    A thin uniform rod $1 \mathrm{~m}$ long has mass $1 \mathrm{~kg}$. Find its moment of inertia and radius of gyration for rotation about a transverse axis through a point midway between its centre and one end.
    View Solution