Question

A force F =(3i – 6j + 2k) N acting on a body produces an acceleration of 3.5 m/s. The mass of the body is (A) 1 kg (B) 2 kg (C) 4 kg (D) 24.5 kg​

Answer 1

Answer:

$\implies \sf\overrightarrow{F} = (3\widehat{i} - 6\widehat{j} + 2\widehat{k}) \: N$

Magnitude of Force :

$\implies \sf | \overrightarrow{F}| = \sqrt{ {(3)}^{2} + {( - 6)}^{2} + {(2)}^{2} }$

$\implies \sf | \overrightarrow{F} | = \sqrt{ 9 + 36 + 4 }$

$\implies \sf | \overrightarrow{F} | = \sqrt{ 49 }$

$\implies \underline{ \boxed{ \red{\bf | \overrightarrow{F} | = 7 \: N }}}$

Mass of body :

$\implies \sf F = ma$

$\implies \sf m = \dfrac{F}{a}$

• Force (F) = 7 N
• Acceleration (a) = 3.5 m/s²

$\implies \sf m = \dfrac{7}{3.5}$

$\implies \underline{ \boxed{ \orange{\bf m = 24.5\: kg }}}$