Advertisements
Advertisements
प्रश्न
A pendulum having a bob of mass m is hanging in a ship sailing along the equator from east to west. When the ship is stationary with respect to water the tension in the string is T0. (a) Find the speed of the ship due to rotation of the earth about its axis. (b) Find the difference between T0 and the earth's attraction on the bob. (c) If the ship sails at speed v, what is the tension in the string? Angular speed of earth's rotation is ω and radius of the earth is R.
Advertisements
उत्तर
(a) Speed of the ship due to rotation of the Earth is v = ωR, where R is the radius of the Earth and ω is its angular speed.
(b) The tension in the string is given by
T0 = mg − mω2R
∴ T0 − mg = mω2R
(c) Let the ship move with a speed v.
Then the tension in the string is given by
\[T = mg - m \omega_1^2 R\]
\[ = T_0 - \frac{\left( v - \omega R \right)^2}{R^2}R\]
\[ = T_0 - \frac{\left( v^2 + \omega^2 R^2 - 2\omega Rv \right)}{R}R\]
\[ \therefore T = T_0 + 2 \ \omega { vm }\]
APPEARS IN
संबंधित प्रश्न
As the earth rotates about its axis, a person living in his house at the equator goes in a circular orbit of radius equal to the radius of the earth. Why does he/she not feel weightless as a satellite passenger does?
Two satellites A and B move round the earth in the same orbit. The mass of B is twice the mass of A.
A body stretches a spring by a particular length at the earth's surface at the equator. At what height above the south pole will it stretch the same spring by the same length? Assume the earth to be spherical.
A Mars satellite moving in an orbit of radius 9.4 × 103 km takes 27540 s to complete one revolution. Calculate the mass of Mars.
Answer the following question.
Define the binding energy of a satellite.
Draw a labelled diagram to show different trajectories of a satellite depending upon the tangential projection speed.
Answer the following question in detail.
What is a critical velocity?
Describe how an artificial satellite using a two-stage rocket is launched in an orbit around the Earth.
Solve the following problem.
Calculate the speed of a satellite in an orbit at a height of 1000 km from the Earth’s surface.
(ME = 5.98 × 1024 kg, R = 6.4 × 106 m)
Solve the following problem.
Calculate the value of acceleration due to gravity on the surface of Mars if the radius of Mars = 3.4 × 103 km and its mass is 6.4 × 1023 kg.
Solve the following problem.
Calculate the value of the universal gravitational constant from the given data. Mass of the Earth = 6 × 1024 kg, Radius of the Earth = 6400 km, and the acceleration due to gravity on the surface = 9.8 m/s2.
Reason of weightlessness in a satellite is ____________.
A geostationary satellite is orbiting the earth at the height of 6R above the surface of earth. R being radius of earth. The time period of another satellite at a height of 2.5 R from the surface of earth is ____________.
A satellite of mass 'm' is revolving around the earth of mass 'M' in an orbit of radius 'r' with constant angular velocity 'ω'. The angular momentum of the satellite is ______.
(G =gravitational constant)
A satellite is revolving in a circular orbit around the earth has total energy 'E'. Its potential energy in that orbit is ______.
Show the nature of the following graph for a satellite orbiting the earth.
- KE vs orbital radius R
- PE vs orbital radius R
- TE vs orbital radius R.
A satellite is revolving in a circular orbit at a height 'h' above the surface of the earth of radius 'R'. The speed of the satellite in its orbit is one-fourth the escape velocity from the surface of the earth. The relation between 'h' and 'R' is ______.
A satellite is revolving around a planet in a circular orbit close to its surface and ρ is the mean density and R is the radius of the planet, then the period of ______.
(G = universal constant of gravitation)
Which of the following is an example of a communication (geostationary) satellite launched by India?
