Question

36. A force F = (31 +4j+5k) N produces
an acceleration of
1.414 m/s2 in a body. What is the mass
of the body?
(a) 3 kg
(b) 4 kg
(c) 5 kg
(d) 10 kg​

Answer 1

$\huge{\mathbb{\red{ANSWER:-}}}$

Given :-

For a body -

$\sf{\vec{F} = (3i + 4j + 5k) \: N}$

$\sf{a = 1.414 \: m/s^{2}}$

To Find :-

$\sf{mass \: of \: the \: body(m) = ?}$

Using Formula :-

From second law of Newton's motion-

$\sf{Force = mass\times acceleration}$

Explanation :-

$\sf{| \vec{F} | =\sqrt{3^{2} + 4^{2} + 5^{2}}}$

$\sf{F =\sqrt{9 + 16 + 25}}$

$\sf{F =\sqrt{50}}$

$\sf{F =5\sqrt{2} \: N}$

$\sf{From \: Newton's \: Second \: law-}$

$\sf{F = ma}$

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

$\sf{m =\dfrac{5\sqrt{2}}{1.414}}$

We know that :-

$\sf{1.414 =\sqrt{2}}$

$\sf{So \: ,}$

$\sf{m =\dfrac{5\sqrt{2}}{\sqrt{2}}}$

$\sf{m = 5 \: kg}$

As We got :-

$\sf{mass \: of \: the \: body \: is \: 5 \: kg.}$

Answer 2

The correct option is 5kg, so option (c) is correct.

Given: F = (3i+4j+5k)

           acceleration = 1.414ms⁻²

To find: mass of the body

Solution: Force = 3i+4j+5k

                           =$\sqrt{3^2+ 4^2 + 5^2$

                            = $\sqrt{9+16+25$

                           = $\sqrt{50$

                          = 5$\sqrt{2$ N

Force = mass× acceleration

5√2 = √2× mass

5 = mass

5kg = mass

Therefore, the correct answer is 5kg and the correct option is (c)