Video Transcript
The given figure represents a group
of masses and their weights on two planets, P and Q. If a body weighs 850 newtons on
planet Q, which of the following is true about the body’s mass and its weight on
planet P? (A) The mass of the body is 85
kilograms and its weight on planet P is 1,700 newtons. (B) The mass of the body is 170
kilograms and its weight on planet P is 425 newtons. (C) The mass of the body is 170
kilograms and its weight on planet P is 1,700 newtons. (D) The mass of the body is 85
kilograms and its weight on planet P is 425 newtons.
This question is asking us to find
the mass of a body and then calculate how much it would weigh on planet P. Before we jump into this question,
let’s check we understand what we’re being asked to do. Recall that the weight of a body is
the gravitational force that acts on the body. Mathematically, the weight, 𝑤, of
a body is equal to the mass of the body, 𝑚, multiplied by the strength of the
gravitational field that the body is in, 𝑔. You might recall that on Earth, 𝑔
has a value of 9.8 newtons per kilogram. But the value of 𝑔 is different on
other planets, because it depends on the planet’s mass and size. This means that two identical
bodies that both have the exact same mass can have different weights on different
planets.
In this question, we’ve been given
a graph that shows the relation between mass and weight on two different planets,
known as P and Q. Mass is shown on the horizontal
𝑥-axis, and weight is shown on the vertical 𝑦-axis. We’ve been told that when a body is
on planet Q, its weight is 850 newtons. We need to work out the mass of the
body and then find what it would weigh if it were on planet P.
Let’s start by working out the mass
of the body. First, we need to find the
gravitational field strength on the planet Q. Remember the formula that we
discussed before: 𝑤 equals 𝑚𝑔. To make it clearer that we’re
talking about planet Q, we’ll label the weight and the gravitational strength on
planet Q with a subscript Q. We don’t need to label the mass of
the body in this way because the mass of the body is the same on both planets.
To find the gravitational field
strength on planet Q, we simply need to rearrange this formula to get 𝑔 sub Q on
its own. We can do this by simply dividing
both sides of the equation by the mass 𝑚. This leaves us with the formula 𝑔
sub Q is equal to 𝑤 sub Q divided by 𝑚. In order to actually calculate 𝑔
sub Q, we need to know a pair of values, a mass and a corresponding weight, for
planet Q. We can get these values from the
graph by picking any point on this line and reading off its 𝑥- and 𝑦-value. For example, let’s pick this point
here at the end of the line.
If we draw a vertical line down to
meet the 𝑥-axis, we see that this point corresponds to a mass of 80 kilograms. If we draw a horizontal line across
to meet the 𝑦-axis, we see that this mass has a weight of 400 newtons. If we substitute these values into
our equation, we find that the gravitational field strength on planet Q is 400
newtons divided by 80 kilograms. So the value of 𝑔 sub Q is equal
to five newtons per kilogram.
Now we’ve calculated the value of
𝑔 sub Q, we can use this to work out the mass of the body in the question. If we go back to the equation 𝑤
sub Q equals 𝑚 multiplied by 𝑔 sub Q, we can rearrange this to make the mass the
subject by dividing both sides of the equation by 𝑔 sub Q. This leaves us with the equation 𝑚
is equal to 𝑤 sub Q divided by 𝑔 sub Q. We know that on planet Q, the body
has a weight of 850 newtons and that 𝑔 sub Q is five newtons per kilogram. Substituting these values into the
formula, we find that the mass of the body is equal to 850 newtons divided by five
newtons per kilogram. This gives us an answer of 170
kilograms.
Now we know that the mass of the
body is 170 kilograms, we just need to work out what it would weigh on planet P. To do this, we need to work out the
strength of the gravitational field on planet P. Just like before, we can do this by
choosing a point on the line for planet P and reading off its 𝑥- and 𝑦-values. Let’s pick this point here at the
end of the line. If we draw a vertical line down to
meet the 𝑥-axis, we see that this point corresponds to a mass of 40 kilograms. If we draw a horizontal line across
to meet the 𝑦-axis, we see that this mass has a weight of 400 newtons. If we substitute these values into
our equation for the gravitational field strength, we find that 𝑔 sub P is equal to
400 newtons divided by 40 kilograms. So 𝑔 sub P is 10 newtons per
kilogram.
We now have everything we need to
work out how much this body weighs on planet P. Going back to the formula for
weight, the weight of the body on planet P, 𝑤 sub P, is simply equal to the mass of
the body, 170 kilograms, multiplied by the gravitational field strength on planet P,
which we’ve just found is 10 newtons per kilogram. Working this through, we find that
the weight of the body on planet P is equal to 1,700 newtons. Looking back at the options, we can
see that this corresponds to statement (C). The mass of the body is 170
kilograms and its weight on planet P is 1,700 newtons. So the correct answer is (C).
