Advertisements
Advertisements
Question
An apple falls from a tree. An insect in the apple finds that the earth is falling towards it with an acceleration g. Who exerts the force needed to accelerate the earth with this acceleration g?
Advertisements
Solution
The mutual gravitational force between the apple and the Earth is responsible for the acceleration produced in the apple falling from the tree. Although the Earth will experience the same force, it does not get attracted towards the apple because of its large mass. The insect feels that the Earth is falling towards the apple with an acceleration g because of the the relative motion.
let
vae = velocity of apple w.r.t earth
\[V_{ea} = \text {velocity of earth w . r . t apple }\]
\[v_{ae} = v_a - v_e = - ( v_e - v_a ) = - v_{ea}\]
As the insect is in the frame of apple so he sees the earth moving with a relative velocity \[v_{ea}\].
Any other observer on earth will see the apple moving towards earth with velocity \[v_{ae}\].
Both are opposite in direction.
APPEARS IN
RELATED QUESTIONS
Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighed 250 N on the surface?
Is there any meaning of "Weight of the earth"?
If heavier bodies are attracted more strongly by the earth, why don't they fall faster than the lighter bodies?
The earth revolves round the sun because the sun attracts the earth. The sun also attracts the moon and this force is about twice as large as the attraction of the earth on the moon. Why does the moon not revolve round the sun? Or does it?
The acceleration of moon with respect to earth is 0⋅0027 m s−2 and the acceleration of an apple falling on earth' surface is about 10 m s−2. Assume that the radius of the moon is one fourth of the earth's radius. If the moon is stopped for an instant and then released, it will fall towards the earth. The initial acceleration of the moon towards the earth will be
The acceleration of the moon just before it strikes the earth in the previous question is
Suppose, the acceleration due to gravity at the earth's surface is 10 m s−2 and at the surface of Mars it is 4⋅0 m s−2. A 60 kg passenger goes from the earth to the Mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky. Which part of the following figure best represents the weight (net gravitational force) of the passenger as a function of time?
If the acceleration due to gravity at the surface of the earth is g, the work done in slowly lifting a body of mass m from the earth's surface to a height R equal to the radius of the earth is
Take the effect of bulging of earth and its rotation in account. Consider the following statements :
(A) There are points outside the earth where the value of g is equal to its value at the equator.
(B) There are points outside the earth where the value of g is equal to its value at the poles.
What is the acceleration due to gravity on the top of Mount Everest? Mount Everest is the highest mountain peak of the world at the height of 8848 m. The value at sea level is 9.80 m s−2.
Find the acceleration due to gravity in a mine of depth 640 m if the value at the surface is 9.800 m s−2. The radius of the earth is 6400 km.
A body is weighed by a spring balance to be 1.000 kg at the North Pole. How much will it weigh at the equator? Account for the earth's rotation only.
Explain the variation of g with latitude.
Calculate the change in g value in your district of Tamil nadu. (Hint: Get the latitude of your district of Tamil nadu from Google). What is the difference in g values at Chennai and Kanyakumari?
One can easily weigh the earth by calculating the mass of the earth by using the formula:
If R is the radius of the earth and g is the acceleration due to gravity on the earth's surface, the mean density of the earth is ______.
A pebble is thrown vertically upwards from the bridge with an initial velocity of 4.9 m/s. It strikes the water after 2 s. If acceleration due to gravity is 9.8 m/s2. The height of the bridge and velocity with which the pebble strikes the water will respectively be ______.
The percentage decrease in the weight of a rocket, when taken to a height of 32 km above the surface of the earth will, be ______.
(Radius of earth = 6400 km)
The mass of a planet is `1/10`th that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is ______.
