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
An aircraft executes a horizontal loop of radius 1.00 km with a steady speed of 900 km/h. Compare its centripetal acceleration with the acceleration due to gravity.
A piece of stone tied at the end of a thread is whirled in a horizontal circle with uniform speed by hand. Answer the following questions:
- Is the velocity of stone uniform or variable?
- Is the acceleration of stone uniform or variable?
- What is the direction of acceleration of stone at any instant?
- Which force provides the centripetal force required for circular motion?
- Name the force and its direction which acts on the hand.
Complete a sentence and explain it.
When an object is in uniform circular motion, its ______ changes at every point.
Answer the following question.
Show that its time period is given by, 2π`sqrt((l cos theta)/("g"))` where l is the length of the string, θ is the angle that the string makes with the vertical, and g is the acceleration due to gravity.
A particle goes round a circular path with uniform speed v. After describing half the circle, what is the change in its centripetal acceleration?
The ratio of angular speed of a hour-hand to the second-hand of a watch is ____________.
A particle is moving in uniform circular motion with speed 'V' and radius 'R'. The angular acceleration of the particle is ______.
A wheel is 0.25 m in radius. When it makes 15 revolutions per minute, its linear speed at the point on circumference is ____________.
Select the WRONG statement.
At any instant, the magnitude of the centripetal force on a particle of mass 'm' performing circular motion is given by (ω = angular velocity and v = linear velocity of the particle) ______.
A mass 'm' is tied to one end of a spring and whirled in a horizontal circle with constant angular velocity. The elongation in the spring is 1 cm. If the angular speed is doubled, the elongation in the spring is 6 cm. The original length of the spring is ______.
The angular speed of the minute hand of a clock in degrees per second is ______.
A wet open umbrella is held upright and is rotated about the handle at a uniform rate of 21 revolutions in 44 s. If the rim of the umbrella is a circle of 1 metre in diameter and the height of the rim above the floor is 1.5 m, the drops of water spun off the rim and hit the floor at a horizontal ______ m from the umbrella.
The distance of the Sun from earth is 1.5 × 1011 m and its angular diameter is (2000) s when observed from the earth. The diameter of the Sun will be ______.
Angular speed of hour hand of a clock in degree per second is ______.
The acceleration of a point on the rim of a flywheel 1 m in diameter, if it makes 1200 rpm is ______.
A wheel is Subjected to uniform angular acceleration about its axis. Initially. its angular velocity is zero. In the first 2 s, it rotates through an angle θ1, in the next 2 s, it rotates through an angle θ2. The ratio of `theta_2/theta_1` is ______.
Explain the meaning of uniform circular motion.
In uniform circular motion, although the speed is constant, why does acceleration occur?
What is the direction of the velocity of an object at any point during uniform circular motion?
