What is the change of value of g with the depth of earth explain with derivation.
Asked by yashwantjain12 | 7th Dec, 2015, 11:25: AM
Considering the Earth to be a homogenous sphere of radius R and mass M.
Let ρ be the mean density of the Earth.
g be acceleration due to gravity.
Consider the body at the depth 'd' from the surface of the Earth where the value of acceleration due to gravity is g'.
Here, the force of gravity acting on the body is only due to inner solid sphere of radius (R-d) and mass be M'.
Dividing (2) by (1), we get,
If we go down in a mine of depth 'd' , the value of 'g' decreases due to decreased mass of attracting Earth.
At the centre of the Earth, the value of g becomes be zero.
Answered by Faiza Lambe | 7th Dec, 2015, 11:43: PM
- A planet moves around the earth in nearly circular orbit. Its period of revolution ‘T’ depends upon: (i) radius ‘r’ of the earth (ii) mass ‘m’ of the sun (iii) the gravitational constant ‘G’. Show dimensionally that T2 DIRECTLY PROPORTIONAL TO r3
- A woman of mass 50 kg is standing in an elevator. Suddenly the cable of the elevator break and the elevator begin to fall freely .the force exerted by the floor of the elevator on the woman is?
- Derive an expression for variation of g with depth
- State the Newton's Law of Gravitation. Also state its important properties.
- Which law explains the rotation of planets around the sun and the rotation of satellites around the planets?
- Define gravitational constant.
- Two bodies of mass 1kg and 2kg kept 4m apart exert a force of F Newton. A third body of mass 3kg is introduced in the set up and kept near 2kg mass. Calculate the total force on the 1kg body.
- On which two quantities does the gravitational force depend?
- Consider two bodies X and Y with mass m1 and m2 separated by distance ‘r’ meters. Suppose mass of X is doubled and mass of Y is tripled also the distance between them is doubled. Find the ratio of the gravitational force before and after changing the masses and distance.
Kindly Sign up for a personalised experience
- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions
Verify mobile number
Enter the OTP sent to your number