Advertisements
Advertisements
प्रश्न
Earth also moves in circular orbit around sun once every year with on orbital radius of 1.5 × 1011 m. What is the acceleration of earth (or any object on the surface of the earth) towards the centre of the sun? How does this acceleration compare with g = 9.8 m/s2?
Advertisements
उत्तर
The orbital radius of the earth around the sun (R) = 1.5 × 1011 m
Time period = 1 yr = 365 day
= 365 × 24 × 60 × 60 s
= 3.15 ×107 s
Centripetal acceleration `(a_c) = Rω^2 = (5pi^2R)/T^2`
= `(4 xx (22/7)^2 xx 1.5 xx 10^11)/(3.15 xx 10^7)^2`
= `5.97 xx 10^-3` m/s2
∴ `a_c/g = (5.97 xx 10^-3)/9.8 = 1/1642`
APPEARS IN
संबंधित प्रश्न
In U. C. M (Uniform Circular Motion), prove the relation `vec v = vec w xx vec r`, where symbols have their usual meanings.
A particle starts from the origin at t = 0 s with a velocity of 10.0 `hatj "m/s"` and moves in the x-y plane with a constant acceleration of `(8.0 hati + 2.0 hatj) ms^(-2)`.
- At what time is the x-coordinate of the particle 16 m? What is the y-coordinate of the particle at that time?
- What is the speed of the particle at the time?
A vehicle is moving on a circular track whose surface is inclined towards the horizon at an angle of 10°. The maximum velocity with which it can move safely is 36 km / hr. Calculate the length of the circular track. [π = 3.142]
Solve the following problem.
A projectile is thrown at an angle of 30° to the horizontal. What should be the range of initial velocity (u) so that its range will be between 40m and 50 m? Assume g = 10 m s-2.
The angle subtended by the vector A = `5hat"i" + 3hat"j" + 12hat"k"` with the X-axis is ______.
The ratio of angular speed of a hour-hand to the second-hand of a watch is ____________.
The ratio of the angular speed of minute hand and hour hand of a watch 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 ____________.
A string of length 'l' fixed at one end carries a mass 'm' at the other end. The string makes `3/pi` revolutions/second around the vertical axis through the fixed end as shown in figure. The tension 'T' in the string is ______.
The angular speed of the minute hand of a clock in degrees per second is ______.
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 ______.
The given graph represents motion with ______ speed.
It is possible to have objects moving with uniform velocity but non-uniform acceleration.
A body moving along a circular path of radius R with velocity v, has centripetal acceleration a. If its velocity is made equal to 2v. What will be the centripetal acceleration?
For a particle performing uniform circular motion, choose the correct statement(s) from the following:
- Magnitude of particle velocity (speed) remains constant.
- Particle velocity remains directed perpendicular to radius vector.
- Direction of acceleration keeps changing as particle moves.
- Angular momentum is constant in magnitude but direction keeps changing.
A ceiling fan rotates about its own axis with some angular velocity. When the fan is switched off the angular velocity becomes `(1/4)^"th"` of the original in time 't' and 'n' revolutions are made in that time. The number of revolutions made by the fan during the time interval between switch off and rest are ______. (Angular retardation is uniform)
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 ______.
Explain the meaning of uniform circular motion.
Angular displacement is measured in which unit?
