Law of Gravitation QA 3
Download as PPTX, PDF0 likes166 views
The document presents a physics problem about a bullet fired vertically upwards from a spherical planet and discusses its maximum height where gravity is reduced to a quarter of its surface value. It calculates the escape velocity from the planet's surface using gravitational equations and energy conservation principles. The correct option for escape velocity is derived as (b) 2(v/r).
![Physics Helpline
L K Satapathy Gravitation QA 3
Correct option = (b)
21
2 2
GMm GMm
mv
R R
21
2 2
GMm
mv
R
GM
v
R
]2 [
2
e
GM
v v
R
Ans
Velocity of projection from surface = v 21
2
K mv
Potential energy on the surface is
GMm
U
R
Total energy on the surface is 21
2
GMm
E mv
R
At height h = R , it stops. KE = 0 and PE
2
GMm
R
Total energy
2
GMm
R
Conservation of energy gives
Escape velocity from the surface is](https://image.slidesharecdn.com/gravitation3-160711050432/85/Law-of-Gravitation-QA-3-3-320.jpg)
Law of Gravitation QA 3
- 1. Physics Helpline L K Satapathy Gravitation QA 3 Escape Velocity 2 e GM v R
- 2. Physics Helpline L K Satapathy Gravitation QA 3 Question : A bullet is fired vertically upwards with velocity v from the surface of a spherical planet . When it reaches its maximum height , its acceleration due to the planet’s gravity is (1/4)th of its value at the surface of the planet . Then the escape velocity from the surface of the planet is ( ) 2 ( ) 2 ( ) ( ) ( 2 1) 2 v a v b v c d v Answer : 2 ' . . . (2) ( ) GM g R h 2 2 4 ( ) 4 g GM GM g R h R Mass of earth = M , Radius of earth = R , Let mass of bullet = m Acceleration due to gravity on the surface of earth is 2 . . . (1) GM g R At a height h , acceleration due to gravity becomes It is given that 2 2 ( ) 4R h R 2R h R h R
- 3. Physics Helpline L K Satapathy Gravitation QA 3 Correct option = (b) 21 2 2 GMm GMm mv R R 21 2 2 GMm mv R GM v R ]2 [ 2 e GM v v R Ans Velocity of projection from surface = v 21 2 K mv Potential energy on the surface is GMm U R Total energy on the surface is 21 2 GMm E mv R At height h = R , it stops. KE = 0 and PE 2 GMm R Total energy 2 GMm R Conservation of energy gives Escape velocity from the surface is
- 4. Physics Helpline L K Satapathy For More details: www.physics-helpline.com Subscribe our channel: youtube.com/physics-helpline Follow us on Facebook and Twitter: facebook.com/physics-helpline twitter.com/physics-helpline