Question

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

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Answer 1

$\huge \underline \mathfrak {Solution:-}$

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 = 2 m/s^2

We know that,

Force = mass × acceleration

$mass = \frac{force}{acceleration} \\ \\mass = \frac{14.142}{2} \\ \\ mass = 7.071 \: kg$So, the mass of the object is of 7.071 kg.