A force F = 8i -6j -10k newton produces acceleration of 1 m s-2 in a body. The mass of the body is:
Correct answer: B. 10√2kg
- A. 10kg
- B. 10√2kg
- C. 10√3kg
- D. 200kg
Explanation
To solve the problem, first calculate the magnitude of the force vector F = 8i - 6j - 10k. The magnitude |F| is calculated as: |F| = √(82 + (-6)2 + (-10)2) = √(64 + 36 + 100) = √200 = 10√2 N. Using Newton's second law, F = ma, where F is the magnitude of the force, m is the mass, and a is the acceleration (1 m/s2). Thus, we have:10√2 = m x 1Therefore, m = 10√2 kg.Option B is correct. Option A is incorrect because it assumes a different force magnitude. Option C is incorrect as it results from a miscalculation of the force magnitude. Option D is incorrect because it suggests an unreasonably large mass given the force and acceleration.
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