Question

State whether a given statement is true or False.
Weight remains constant at all places.
A. True
B. False

Answer 1

Hint: Here we will first see what is weight. After this we will define the term’ acceleration due to gravity(g)’. From the formula of ‘g’, we will discuss its variation. This will give a clear idea about the weight at different places.

Complete Step-by-Step solution:
First of all, we will see what is weight.
Weight of an object is defined as the product of mass of the object(m) and acceleration due to gravity(g).
W = mg
m = Mass of object
g= acceleration due to gravity.
W = weight of object.
Now, we see the definition of ‘g’.
Acceleration due to gravity is the acceleration gained by an object due to the gravitational force. Its SI unit is m/$s^2$. It has both magnitude and direction, hence, it’s a vector quantity. Acceleration due to gravity is represented by g.
The formula for ‘g’ is given as:
${\text{g = }}\dfrac{{{\text{GM}}}}{{{r^2}}}$
Where,
G = Universal gravitational constant($6.67 \times {10^{ - 11}}{\text{N}}{{\text{m}}^2}/k{g^2}$)
M = Mass of Earth
r = Radius of Earth.
g = acceleration due to gravity of Earth.
So weight can written as:
W = $\dfrac{{{\text{GMm}}}}{{{r^2}}}$ .
Now we will discuss the variation of weight:
From the above formula, we can say that acceleration due to gravity at a place is inversely proportional to the square of the distance of the point from the centre of earth .
Now, the earth is not perfectly spherical. It is flattened at the poles and elongated on the equatorial region.
Hence the weight is maximum at the poles and minimum at the equator. As we move from the equator to the poles, the value of ‘g’ increases and hence the weight increases.
Hence we can say that the weight is not constant at all places.
So, the given statement is false.

Note- In this type of question, you should remember the formula for acceleration due to gravity. It should be noted that the value of g decreases with increase in height of an object and the value of g becomes zero at infinite distance from the earth. The weight of an object on the moon is 1/6th of the weight on the earth surface.