Advertisements
Advertisements
प्रश्न
Find the acceleration of a particle placed on the surface of the earth at the equator due to earth's rotation. The diameter of earth = 12800 km and it takes 24 hours for the earth to complete one revolution about its axis.
Advertisements
उत्तर
Diameter of the Earth = 12800 km
So, radius of the Earth, R = 6400 km = 6.4 × 106 m
Time period of revolution of the Earth about its axis :
\[T = 24 \text{hr} = 24 \times 3600 \text{s}\]
\[\text{v} = \frac{2\pi r}{T}=\frac{2 \times 3 . 14 \times 64 \times {10}^6}{24 \times 3600}\]
\[\Rightarrow \text{v} = 465 . 185 \text{ m/s}\]
\[\text { Acceleration of the particle }: \]
\[a = \frac{v^2}{R} = \frac{\left( 465 . 185 \right)^2}{64 \times {10}^5} = 0 . 038 \text{ m/ s}^2\]
APPEARS IN
संबंधित प्रश्न
A 70 kg man stands in contact against the inner wall of a hollow cylindrical drum of radius 3 m rotating about its vertical axis with 200 rev/min. The coefficient of friction between the wall and his clothing is 0.15. What is the minimum rotational speed of the cylinder to enable the man to remain stuck to the wall (without falling) when the floor is suddenly removed?
When a particle moves in a circle with a uniform speed
Water in a bucket is whirled in a vertical circle with string attached to it. The water does no fall down even when the bucket is inverted at the top of its path. We conclude that in this position
A stone of mass m tied to a string of length l is rotated in a circle with the other end of the string as the centre. The speed of the stone is v. If the string breaks, the stone will move
A rod of length L is pivoted at one end and is rotated with a uniform angular velocity in a horizontal plane. Let T1 and T2 be the tensions at the points L/4 and 3L/4 away from the pivoted ends.
A table with smooth horizontal surface is fixed in a cabin that rotates with a uniform angular velocity ω in a circular path of radius R (In the following figure). A smooth groove AB of length L(<<R) is made the surface of the table. The groove makes an angle θ with the radius OA of the circle in which the cabin rotates. A small particle is kept at the point A in the groove and is released to move at the point A in the groove and is released to move along AB. Find the time taken by the particle to reach the point B.
A car moving at a speed of 36 km/hr is taking a turn on a circular road of radius 50 m. A small wooden plate is kept on the seat with its plane perpendicular to the radius of the circular road (In the following figure). A small block of mass 100 g is kept on the seat which rests against the plate. the friction coefficient between the block and the plate is. (a) Find the normal contact force exerted by the plate on the block. (b) The plate is slowly turned so that the angle between the normal to the plate and the radius of the road slowly increases. Find the angle at which the block will just start sliding on the plate.
A person stands on a spring balance at the equator. If the speed of earth's rotation is increased by such an amount that the balance reading is half the true weight, what will be the length of the day in this case?
When seen from below, the blades of a ceiling fan are seen to be revolving anticlockwise and their speed is decreasing. Select the correct statement about the directions of its angular velocity and angular acceleration.
A particle of mass 1 kg, tied to a 1.2 m long string is whirled to perform the vertical circular motion, under gravity. The minimum speed of a particle is 5 m/s. Consider the following statements.
P) Maximum speed must be `5sqrt5` m/s.
Q) Difference between maximum and minimum tensions along the string is 60 N.
Select the correct option.
Two particles A and B are located at distances rA and rB respectively from the centre of a rotating disc such that rA > rB. In this case, if angular velocity ω of rotation is constant, then ______
A child starts running from rest along a circular track of radius r with constant tangential acceleration a. After time the feels that slipping of shoes on the ground has started. The coefficient of friction between shoes and the ground is [g = acceleration due to gravity].
A rope is wound around a solid cylinder of mass 1 kg and radius 0.4 m. What is the angular acceleration of cylinder, if the rope is pulled with a force of 25 N? (Cylinder is rotating about its own axis.)
A body is moving along a circular track of radius 100 m with velocity 20 m/s. Its tangential acceleration is 3 m/s2, then its resultant acceleration will be ______.
The centripetal force of a body moving in a circular path, if speed is made half and radius is made four times the original value, will ____________.
When a body slides down from rest along a smooth inclined plane making an angle of 45° with the horizontal, it takes time T. When the same body slides down from rest along a rough inclined plane making the same angle and through the same distance, it is seen to take time pT, where p is some number greater than 1. Calculate the co-efficient of friction between the body and the rough plane.
A block of 200 g mass moves with a uniform speed in a horizontal circular groove, with vertical side walls of radius 20 cm. If the block takes 40 s to complete one round, the normal force by the side walls of the groove is ______.
A stone tide to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is `sqrt(x("u"^2 - "gL")`. The value of x is ______.
