Question

A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 m/s. The magnitude of its momentum is recorded as
A. 17.56kgm/s
B. 17.57kgm/s
C. 17.6kgm/s
D. 17.565kgm/s

Answer 1

We have a body moving along the x – axis. The mass and speed of the body is given to us. To calculate the linear momentum of the body, we know the equation for linear momentum. We also need to consider the significant figures in the value of mass and speed of the body. Thus we get the solution.

Formula used: Linear momentum,
$p=m\times v$

Complete step by step answer:
In the given question we have a body that is moving along the x-axis.
The mass of the body and its speed is given to us,
Mass, m = 3.513 kg
Speed, v = 5.00 m/s
We need to find the magnitude of the linear momentum of the body.
We know the equation for magnitude of linear momentum,
$p=m\times v$, where ‘p’ is linear momentum, ‘m’ is mass of the body, ‘v’ is speed of the body.
Therefore,
$p=\left( 3.513kg \right)\left( 5.00m/s \right)$
Here when we substitute for mass and speed, we should substitute them considering the significant figures in them.
By solving this we get momentum as,
$p=17.565kgm/s$
But this is not the actual value of momentum.
According to the multiplication of significant figures, when we multiply two significant figures the result should contain the least significant figure.
Considering this case, the value of mass is, m = 3.153 has 4 significant figures and the value of speed, v=5.00 has 3 significant figures.
Therefore the result of their product should contain only 3 significant figures.
Here we got the linear momentum, p = 17.565kgm/s.
This contains 5 significant figures.
Hence we should round it to 3 significant figures.
Therefore we get linear momentum as,
$p=17.6kgm/s$

So, the correct answer is “Option C”.

Note: In this question the options are given with small variations in decimals. Hence it is important to consider the significant figures.
If in any question the options come with small variations in the decimals always consider the significant figures and round off the result according to the significant figures.