Problem solving tips

## Gravitation

- Want to score better marks in exams? Have a look at some problem solving tips.
1
Tip 1: Problem related to universal law of gravitation:
• The universal law of gravitation includes only one formula i.e. .
• If the force or the ratio of force between the two conditions is to be determined, then find out the quantities that remains constant in two situations.
• While taking the ratio, the constant quantities will be eliminated and the remaining change in the parameters can be addressed in terms of one another to make the solution simple and comprehensive.
Let's practice some problems based on it:
Two lead spheres of same radius are in contact with each other. The gravitational force of attraction between them is F. If two lead spheres of double the previous radius are in contact with each other, the gravitational force of attraction between them will be:
A
B
C
D
The gravitational force of attraction between two bodies at a certain distance is . If the distance between them is doubled, the force of attraction:
A
decreases by
B
decreases by
C
increases by
D
increases by
2
Tip 2: Problem related to calculation of change in value of acceleration due to gravity (due to height).
• The value of 'g' with the change in height above the surface of the Earth or with the increasing altitude is given in two different manner.
• Thus, it is very necessary to keep in mind if the height is comparable to the radius of Earth or not and then use appropriate formula.
Let's practice some problems based on it:
The value of at a height of from the surface of the Earth is nearly (Radius of the Earth  6400km) ( on the surface of the Earth  )
A
B
C
D
If on the surface of the Earth is , its value at a height of is: (Radius of the Earth )
A
B
C
D
3
Tip 3: Problem related to calculation of change in value of acceleration due to gravity (due to depth).
• The value of acceleration due to gravity changes due to change in depth from the surface of Earth.
• In this cases the value of gravity decreases towards the center using the relation:
• At the center of Earth, the value of 'g' is zero i.e. weightlessness can be experienced at the center of Earth.
Let's practice some problems based on it:
At a place, the value of 'g' is less by 1% than its value on the surface of the Earth (Radius of Earth, ). The place is :
A
64 km below the surface of the earth
B
64 km above the surface of the earth
C
30 km above the surface of the earth
D
32 km below the surface of the earth
If on the surface of the Earth is , then it's value at a depth of (Radius of the earth ) is
A
B
C
D
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Tip 4: Problem based on Kepler's third law.
• The Kepler's third law gives the relation between the time period and orbital distance of the planet.
• We have generally seen the expression of Kepler's third law as: .
• But the elaborated form of the expression with the constants is as:
• The above expression enables us in determining the mass of a particular body around which a planet (or anything) revolves and further determine other parameters.
Let's practice some problems based on it:
For a given density of the planet, the orbital period of a satellite near the surface of planet of radius is proportional to:
A
B
C
D
The distance between the Sun and the Earth is and the Earth takes time to make one complete revolution around the Sun. Assuming the orbit of the Earth around the Sun to be circular, the mass of the Sun will be proportional to
A
B
C
D
5
Tip 5: Problems based on use of formula for gravitational potential energy.
• The use of formula for calculating gravitational potential energy depends on the height or the distance of the body from the surface of the Earth.
• The proper use of the formula and determining parameters is shown in the video added below.
Gravitational Potential Energy Problem Solving Tips
7 mins
Let's practice some problems based on it:
If a body of mass m has to be taken from the surface to the earth to a height h = R, then the amount of energy required is (R = radius of the earth)
A
B
C
D
E
The difference in of an object of mass when it is taken from a height of to from the surface of the earth is
A
J
B
J
C
J
D
J