Back to Directory
NEET PHYSICSEasy

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 accelerates with 1 m/s21 \text{ m/s}^2. What will be the mass of the body?

A

102 kg10\sqrt{2} \text{ kg}

B

210 kg2\sqrt{10} \text{ kg}

C

10 kg10 \text{ kg}

D

20 kg20 \text{ kg}

Step-by-Step Solution

  1. Newton's Second Law: The relationship between force, mass, and acceleration is given by F⃗=ma⃗\vec{F} = m\vec{a}. In terms of magnitude, ∣F⃗∣=m∣a⃗∣|\vec{F}| = m|\vec{a}| [Source 75, 77].
  2. Magnitude of Force Vector: The magnitude of the force vector F⃗=Fxi^+Fyj^+Fzk^\vec{F} = F_x\hat{i} + F_y\hat{j} + F_z\hat{k} is calculated using the formula ∣F⃗∣=Fx2+Fy2+Fz2|\vec{F}| = \sqrt{F_x^2 + F_y^2 + F_z^2} [Source 53, 54]. Substituting the given components (Fx=6,Fy=−8,Fz=10F_x=6, F_y=-8, F_z=10): ∣F⃗∣=(6)2+(−8)2+(10)2|\vec{F}| = \sqrt{(6)^2 + (-8)^2 + (10)^2} ∣F⃗∣=36+64+100=200=102 N|\vec{F}| = \sqrt{36 + 64 + 100} = \sqrt{200} = 10\sqrt{2} \text{ N}
  3. Calculation of Mass: Given the acceleration magnitude a=1 m/s2a = 1 \text{ m/s}^2: m=∣F⃗∣a=1021=102 kgm = \frac{|\vec{F}|}{a} = \frac{10\sqrt{2}}{1} = 10\sqrt{2} \text{ kg}
Practice Mode Available

Master this Topic on Sushrut

Join thousands of students and practice with AI-generated mock tests.

Get Started