Question

A body, under the action of a force $\overrightarrow{F}=6\hat{i}-8\hat{j}+10\hat{k}$, acquires an acceleration of 1 $m/s^2$. The mass of this body must be :

• A. $10\sqrt{2}kg$
• B. $2\sqrt{10}kg$
• C. 10 kg
• D. 20 kg

Answer 1

The correct option is A $10\sqrt{2}kg$

$\text{Step 1: Magnitude of force}$

$\overrightarrow{F}=6\hat{i}-8\hat{j}+10\hat{k}$

$|\overrightarrow{F}|=\sqrt{F_x^2+F_y^2+F_z^2}$

$\Rightarrow |\overrightarrow{F}|=\sqrt{6^2+8^2+{10}^2}$

$\Rightarrow |\overrightarrow{F}|=\sqrt{200}=10\sqrt{2}N$

$\text{Step 2: Calculation of mass}$

Now apply Newton's 2nd Law-

From $F=ma$

$\Rightarrow m=\frac{F}{a}$

$\Rightarrow m=\frac{10\sqrt{2}N}{1m/s^2}$

$m=10\sqrt{2}kg$

Hence, Option (A) is correct