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
Is it necessary for the plane of the orbit of a satellite to pass through the centre of the earth?
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?
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.
What is the true weight of an object in a geostationary satellite that weighed exactly 10.0 N at the north pole?
Answer the following question.
Define the binding energy of a satellite.
Answer the following question.
What do you mean by geostationary satellite?
State the conditions for various possible orbits of satellite depending upon the horizontal/tangential speed of projection.
Answer the following question in detail.
State any four applications of a communication satellite.
Derive an expression for the binding energy of a body at rest on the Earth’s surface of a satellite.
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.
A body weighs 5.6 kg wt on the surface of the Earth. How much will be its weight on a planet whose mass is 7 times the mass of the Earth and radius twice that of the Earth’s radius?
Which of the following statements is CORRECT in respect of a geostationary satellite?
An aircraft is moving with uniform velocity 150 m/s in the space. If all the forces acting on it are balanced, then it will ______.
Is it possibe for a body to have inertia but no weight?
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)
Two satellites of same mass are orbiting round the earth at heights of r1 and r2 from the centre of earth. Their potential energies are in the ratio of ______.
What is the approximate period of revolution for the Moon, Earth's only natural satellite?
What is the typical altitude range for a polar satellite's orbit?
Artificial satellites are launched for all the following purposes EXCEPT:
