Advertisements
Advertisements
प्रश्न
Earth can be thought of as a sphere of radius 6400 km. Any object (or a person) is performing circular motion around the axis of earth due to earth’s rotation (period 1 day). What is acceleration of object on the surface of the earth (at equator) towards its centre? what is it at latitude θ? How does these accelerations compare with g = 9.8 m/s2?
Advertisements
उत्तर
Radius of the earth (R) = 6400 km = 6.4 × 106 m
Time period (T) = 1 day = 24 × 60 × 60 s = 86400 s
Centripetal acceleration (ac) = `ω^2 R = R((2pi)/T)^2 = (4pi^2R)/T`
= `(4 xx (22/7)^2 xx 64 xx 10^6)/(24 xx 60 xx 60)^2`
= `(4 xx 484 xx 64 xx 10^6)/(49 xx (24 xx 3600)^2`
= 0.034 m/s2
At equator, latitude θ = 0°
∴ `a_c/g = 0.034/9.8 = 1/288`
APPEARS IN
संबंधित प्रश्न
Earth moves around the sun with uniform velocity.
A uniform linear motion is unaccelerated, while a uniform circular motion is an accelerated motion.
A uniform metre rule of mass 100g is balanced on a fulcrum at mark 40cm by suspending an unknown mass m at the mark 20cm.
To which side the rule will tilt if the mass m is moved to the mark 10cm ?
Solve the following problem.
A car moves in a circle at a constant speed of 50 m/s and completes one revolution in 40 s. Determine the magnitude of the acceleration of the car.
Is the uniform circular motion accelerated? Give reasons for your answer.
If a particle moves with uniform speed then its tangential acceleration will be ______.
A particle is moving in uniform circular motion with speed 'V' and radius 'R'. The angular acceleration of the particle is ______.
A body of mass ·m' is moving along a circle of radius 'r' with linear speed 'v'. Now, to change the linear speed to `V/2` and to move it along the circle of radius '4r', required change in the centripetal force of the body is ______.
A particle is perfonning uniform circular motion. If 'θ', 'ω', 'α' and ' a' are its angular displacement, angular velocity, angular acceleration, and centripetal acceleration respectively, then which of the following is 'WRONG'?
A cyclist is riding with a speed of 43.2 km/h. As he approaches a circular turn on the road of radius 60 m, he applies brakes and reduces his speed at constant rate of 1.8 ms-2. The magnitude of the net acceleration of the cyclist is ______.
A string of length `l` is fixed at one end and carries a mass 'm' at the other end. The mass is revolving along a horizontal circle of radius 'r' making 'θ' as the semi-vertical angle of cone and `(1/pi)` revolutions per second around the vertical axis through fixed end. The tension in the string is ______.
The given graph represents motion with ______ speed.
A body moves in a uniform circular motion ______.
A particle is performing a uniform circular motion along a circle of radius R. In half the period of revolution, its displacement and distance covered are respectively.
A horizontal circular platform of mass M is rotating at angular velocity ω about a vertical axis passing through its centre. A boy of mass m is standing at the edge of the platform. If the boy comes to the centre of the platform, then the new angular velocity becomes ______.
Two bodies of masses 10 kg and 5 kg moving in concentric orbits of radii R and r such that their periods are the same. Then the ratio between their centripetal accelerations is ______.
A body of mass m is moving in circle of radius r with a constant speed v. The work done by the centripetal force in moving the body over half the circumference of the circle is ______.
What is the direction of the velocity of an object at any point during uniform circular motion?
The relationship between an object's linear velocity (v) and its angular velocity (ω) in a circular path of radius (r) is given by:
