(Slo based Solution)
National Book Foundation
Chapter # 5
Gravitation
(Solved Numerical)
- F=G(m1*m2) / r^2
- gh=gr^2/(r+h)^2
- v= (Gm/(r+h))^1/2
- g=G m/r^2
mass of earth = 6 * 10 ^24
radius of earth = 6.4 * 10 ^ 6
Solve the following numerical questions.
1. Two identical balls of masses 1000 kg each have distance of 50 m between their centers . Find the gravitational force between the balls .
2. Two stars of masses 2 * 10 ^10 kg and 4 * 10 ^20 kg experience gravitational force of 1000 N . Find the separation between the two stars ?
3. Calculate the value of g at the height of 1500 km above the surface of earth ?
Given
h=1500 km=1.5*10^6m
mass of earth = 6.0 * 10 ^ 24 kg
radium of earth = 6.4 * 10 ^6 m
To find gh=?
Calculation
gh=gr^2/(r+h)^2
=(9.8*6.4*10^6*6.4*10^6)/(6.4 * 10 ^6 +1.5* 10^6)^2
=(401.408*10^12)/(7.9 *10^6)^2
=(401.408*10^12)/(62.41*10^12)
=401.408/62.41
=6.4m/s^2
4. A geostationary satellite revolves around the earth in an orbit of the radius 42000 km . Find the value of g and orbital speed at this height ?
Given
h=42000 km=42 * 10^6 m
mass of earth = 6.0 * 10 ^ 24 kg
gh=?
Calculation
gh=gr^2/(r+h)^2
=(9.8*6.4*10^6*6.4*10^6)/(6.4 * 10 ^6 +1.5* 10^6)^2
=(401.408*10^12)/(7.9 *10^6)^2
=(401.408*10^12)/(62.41*10^12)
=401.408/62.41
=6.4m/s^2
4. A geostationary satellite revolves around the earth in an orbit of the radius 42000 km . Find the value of g and orbital speed at this height ?
Given
h=42000 km=42 * 10^6 m
mass of earth = 6.0 * 10 ^ 24 kg
radium of earth = 6.4 * 10 ^6 mTo find g=? v=?Calculation
orbital speed
v= (Gm/(r+h))^1/2
= ( (6.673*10^-11 * 6* 10^24)/(6.4 * 10 ^6+ 42 * 10 ^6) ) ^1/2
=(( 40.038 * 10 ^13) / (48.4 * 10^6))^1/2
v=(0.82723 * 10 ^7 ) ^ 1/2
v=(8.3 * 10 ^ 6 ) ^ 1/2
v=2.9 * 10 ^ 3 m/s =3km/s
Value of g at 42000 km
gh=gr^2/(r+h)^2
=(9.8*6.4*10^6*6.4*10^6)/(6.4 * 10 ^6 +42* 10^6)^2
=(401.408*10^12)/(48.4 *10^6)^2
=401.408/2304
gh=0.17m/s^2
5. Value of g on earth surface is 9.8 m/s^2 . What is the value of g on a planet whose mass is five times the mass of earth and its radius is twice the radius of earth ? what is the weight of 130 kg body on this planet ?
Given mass of planet = 5 * mass of earth = 5* 6 * 10 ^24 =30*10 ^24radius of planet = 2*radius of earth = 2*6.4 * 10 ^6 =12.8 *10 ^6mass of body at planet = 130 kg
To find value of g on planet(g1) =? weight of body on planet (w) = ?
Calculation
g1=G m/r^2 =( 6.673 * 10^-11* 30 * 10 ^24)/(12.8*10^6)^2 =200.19 * 10 ^13/163.84 * 10^12 =12.5 m/s^2w =mg =130*12.5 =1625 N
orbital speed
v= (Gm/(r+h))^1/2
= ( (6.673*10^-11 * 6* 10^24)/(6.4 * 10 ^6+ 42 * 10 ^6) ) ^1/2
=(( 40.038 * 10 ^13) / (48.4 * 10^6))^1/2
v=(0.82723 * 10 ^7 ) ^ 1/2
v=(8.3 * 10 ^ 6 ) ^ 1/2
v=2.9 * 10 ^ 3 m/s =3km/s
Value of g at 42000 km
gh=gr^2/(r+h)^2
=(9.8*6.4*10^6*6.4*10^6)/(6.4 * 10 ^6 +42* 10^6)^2
=(401.408*10^12)/(48.4 *10^6)^2
=401.408/2304
gh=0.17m/s^2
5. Value of g on earth surface is 9.8 m/s^2 . What is the value of g on a planet whose mass is five times the mass of earth and its radius is twice the radius of earth ? what is the weight of 130 kg body on this planet ?
6. Calculate orbital speed of satellite orbiting the earth at the height of 6400 km .
V0=(Gm/(r+h))^1/2
=((6.673 * 10 ^-11 * 6*10^24)/(6.4*10^6 +6.4*10^6))^1/2
=((40.0*10^-11+24)/12.8*10^5)^10
=(3.13 * 10^13-6)^1/2
=(31.3*10^-1 *10^7)^1/2
V0=5.6 km
FAQ
Q.1 What is gravitational constant value ?
Ans 6.673 * 10 ^ -11
Q.2 What is SI Unit of gravitational Constant ?
Ans . Nm^2/kg^2
Q.3 Who derived the law of gravity ?
Ans . Sir Isaac Newton
Q.4 Who actually discovered gravity before newton ?
Ans . Jaipur