Q. (a) Differentiate b/w acceleration due to gravity and universal gravitational constant. Derive a relation between 'g' & 'G'.
(b) State universal law of gravitational.
Q. Define 'inertia'
Q. A shopkeeper show free toys to a child made up of aluminium, steel and wood of same shape and volume. Which one of them would have highest inertia? Why?
(a)
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Universal gravitation constant(G)
1.It is define as the force of attraction acting between two bodies each of unit mass, whose centers are placed unit distance apart.
2. Its value is same throughout the universe .
3. It is a scalar quantity .
4. Its value dose not depends upon the nature and the size of the bodies.
5. Dimensional formula for G is [M-1L3T-2].
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Acceleration due to gravity(g)
1.It is define as the constant acceleration produced in a body when it falls freely under the effect of gravity .
2. its value changes from place to palce.
3. it is a vector quantity.
4. Its value depends upon the nature and the size of the bodies.
5. Dimensional formula for g is [M0L1T-2]. |
F = GMm/r^2
Here F = ma = mg
Therefore,
mg = GMm/r2
Divide both sides by m
g = GM / r2
In above g and G relation
g = acceleration due to gravity of planet
G = universal gravitational constant
M = mass of planet
r = radius of planet
(b) The universal law of gravitation states that the force of attraction between two masses m1 and m2 separated by a distance r is directly proportional to the product of the masses and inversely proportional to the square of the distance between the masses.
That is,
F α m1m2
F α 1/r2
Or, F = Gm1m2/r2
Where, G is a constant called the universal gravitational constant and is equal to 6.67 × 10-11 Nm2/Kg2
(c)Inertia is that property of a body which causes it to remain in it's state of motion in a straight line, or spin or rest, until or unless some external force is applied on it. Inertia is present due to mass.(d)
I think its steel as inertia depends upon mass of an object now clearly
It is given that all have same volume therefore the object with large will have more mass as we know that density of steel is greatest of all thus steel would have higher inertia .
Regards