Looking for classes? Ksquare Career Institute, Bengaluru →
A body, under the action of a force $\vec{F} = 6\hat{i} - 8\hat{j} + 10\hat{k}$, 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
Detailed Solution
Magnitude of the force: $|\vec{F}| = \sqrt{6^2 + (-8)^2 + 10^2} = \sqrt{36 + 64 + 100} = \sqrt{200}$
$|\vec{F}| = 10\sqrt{2}$ N
Newton's second law: $F = ma$, so $m = \frac{F}{a}$
$m = \frac{10\sqrt{2}}{1}$
$m = 10\sqrt{2}$ kg
$|\vec{F}| = 10\sqrt{2}$ N
Newton's second law: $F = ma$, so $m = \frac{F}{a}$
$m = \frac{10\sqrt{2}}{1}$
$m = 10\sqrt{2}$ kg