Uncategorized: Practice Problem & Solution
A body, under the action of a force \(vec{F} = 6hat{i} - 8hat{j} + 10hat{k}\) acquires an acceleration of \(1text{ m/s}^2\). The mass of this body must be: (2009, 1996)
Solution Explained:
To solve this problem, we apply the core principles of Uncategorized. Understanding the underlying formula is key to arriving at the correct answer below:
The magnitude of the force is \(|vec{F}| = sqrt{6^2 + (-8)^2 + 10^2} = sqrt{36+64+100} = sqrt{200} = 10sqrt{2}text{ N}\). According to Newton's second law, \(F = ma\). Given \(a = 1text{ m/s}^2\), so \(m = F/a = frac{10sqrt{2}text{ N}}{1text{ m/s}^2} = 10sqrt{2}text{ kg}\).
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