Grade 11Mechanics
what is relation between height h and depth d for the change in g
what is relation between height h and depth d for the change in g
1 Answer
Arun
At a height of h from the surface of the earth, the gravitational force on an object of mass m is
F = GMm/(R+h)^2
Here (R + h) is the distance between the object and the centre of earth.
Say at that height h, the gravitational acceleration is g1.
So we can write, mg1 = GMm / (R+h)^2
=> g1 = GM/(R+h)^2 _________________ (5)
Now we know on the surface of earth, it is
g = GM / R^2
Taking ratio of these 2,
g1/g = R^2 /(R+h)^2
= 1/(1 + h/R)^2 = (1 + h/R)^(-2) = (1 – 2h/R)
=> g1/g = (1 – 2h/R)
=> g1 = g (1 – 2h/R) ___________________ (6)
So as altitude h increases, the value of acceleration due to gravity falls.
Other Related Questions on mechanics
Three identical balls are placed on a frictionless
horizontal surface touching each other. They stick to
each other because of adhesive. Another ball of same
radius and mass m is placed over the void created by
the three balls. Find the forces applied by the balls
kept on the floor to each other if the system remains
in equilibrium.
Three identical balls are placed on a frictionless
horizontal surface touching each other. They stick to
each other because of adhesive. Another ball of same
radius and mass m is placed over the void created by
the three balls. Find the forces applied by the balls
kept on the floor to each other if the system remains
in equilibrium.
mechanics
Last Activity: 10 Months ago
A car loaded with water having total mass 1000 kg moves on a straight horizontal Road starting from rest under the action of a force of 100 Newton. The water spills throw a small hole in the bottom at a rate of 0.1 KG per second the velocity of cart after 300 seconds is nearly.
11
21
31
41
A car loaded with water having total mass 1000 kg moves on a straight horizontal Road starting from rest under the action of a force of 100 Newton. The water spills throw a small hole in the bottom at a rate of 0.1 KG per second the velocity of cart after 300 seconds is nearly.
11
21
31
41
mechanics
Last Activity: 10 Months ago
A metal strip clamped at one end vibrates with a frequency of 20 Hz and amplitude of 5 mmat the free end, where a small mass of 2 g is positioned. determine(i) The velocity of the end when passing through the zero position(ii) The acceleration at maximum displacement(iii) The maximum kinetic energy of the mass
A metal strip clamped at one end vibrates with a frequency of 20 Hz and amplitude of 5 mm
at the free end, where a small mass of 2 g is positioned. determine
(i) The velocity of the end when passing through the zero position
(ii) The acceleration at maximum displacement
(iii) The maximum kinetic energy of the mass
mechanics
Last Activity: 3 Years ago
If a=x² find the displacement at t =3sec if body velocity at t= 0 sec is 0
If a=x² find the displacement at t =3sec if body velocity at t= 0 sec is 0
mechanics
Last Activity: 3 Years ago