Question

A force vector applied on a mass is represented as F=6i-8j+10k and mass accelerates with 1 m/s^2. What will be the mass of the body?

Answer 1

To find mass of the body we will use magnitude of force formula  

According to question

F = 6i - 8j + 10k  

Magnitude of Force = √ (6² + 8² + 10²)

= 14.14 N

m = F / a

= 14.14 N / 1 m/s^2

= 14.14 kg

Therefore, answer: Mass of the body is 14.14 kg

Answer 2

$\underline \bold{Solution:-}$

Force = 6i - 8j + 10k

It is given in the terms of components of vector.

So, first of all find it's magnitude.

Magnitude of force

$= \sqrt{ {(6)}^{2} + {( - 8)}^{2} + {(10)}^{2} } \\ \\ = \sqrt{36 + 64 + 100} \\ \\ = \sqrt{200} \\ \\ = 14.142 \: newton$

Acceleration = 1 m/s^2

We know that,

Force = mass × acceleration

$mass = \frac{force}{acceleration} \\ \\mass = \frac{14.142}{1} \\ \\ mass = 14.142 \: kg$

So, the mass of the object is 14.142 kg.