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Question: A force vector applied on a mass is represented as \[\vec F = 6\hat i - 8\hat j + 10\hat k\] and acc...

A force vector applied on a mass is represented as F⃗=6i^−8j^+10k^\vec F = 6\hat i - 8\hat j + 10\hat k and acceleration with 11 m/s2. What will be the mass of the body in Kg?
A. 102Kg10\sqrt 2 Kg
B. 210Kg2\sqrt {10} Kg
C. 10Kg10Kg
D. 20Kg20Kg

Explanation

Solution

In this given question we will need the formula for the force which is the result of the second law of motion. So, the force is equal to the multiplication of the mass and the acceleration of the body.

Complete answer:
Given,
The vector of the force,
Acceleration of the body, a=1a = 1 m/s2,
F⃗=6i^−8j^+10k^\vec F = 6\hat i - 8\hat j + 10\hat k, with the help of this vector we can find the value of the magnitude of the force. So now to get the magnitude of force we will proceed as follows,
∣F⃗∣=62+(−8)2+102\left| {\vec F} \right| = \sqrt {{6^2} + {{( - 8)}^2} + {{10}^2}}
⇒∣F⃗∣=36+64+100\Rightarrow \left| {\vec F} \right| = \sqrt {36 + 64 + 100}
⇒∣F⃗∣=200\Rightarrow \left| {\vec F} \right| = \sqrt {200}
⇒∣F⃗∣=102N\Rightarrow \left| {\vec F} \right| = 10\sqrt 2 N
Now we have got the value of the force. We know the formula for the force as follows,
F=maF = ma, where m=m = mass of the body in Kg, a=a = acceleration of the body.
So now putting the values of the acceleration and the force in the above equation, we get
⇒102=m×1\Rightarrow 10\sqrt 2 = m \times 1
⇒1021=m\Rightarrow \dfrac{{10\sqrt 2 }}{1} = m
⇒m=1021\Rightarrow m = \dfrac{{10\sqrt 2 }}{1}
⇒m=102Kg\Rightarrow m = 10\sqrt 2 Kg
So, the mass of the body in Kg is 102Kg10\sqrt 2 Kg.

So, the correct answer is “Option A”.

Note:
Newton's second law of motion formally can be stated as follows: “The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, and the direction of that acceleration will be in the same direction as that of the net force, and inversely proportional to the mass of the object.”
Newton's second law of motion also given some results in the terms of the momentum, which is as follows: “Newton's second law of motion states that the rate of change of the momentum of a body is directly proportional to the force applied, and the direction of this change in momentum will be in the direction of the applied force.”