Question

9. A force of 6i+2j +8k N acting on a body at rest, so that it velocity changes to 15i +10j +20k in 5 seconds, then mass of the body.​

Answer 1

Given :

Initial velocity = zero (i.e., rest)

Final velocity = 15i + 10j + 20k

Applied force = 6i + 2j + 8k

Time interval = 5$\sf{s}$

To Find :

We have to find mass of the body$.$

SoluTion :

First of all, We need to find acceleration of body. It is defined as the rate of change of velocity.

$\implies\sf\:a=\dfrac{v-u}{t}$

$\implies\sf\:a=\dfrac{(15i+10j+20k)-0}{5}$

$\implies\bf\:a=(3i+2j+4k)\:ms^{-2}$

As per Newton's second law of motion, Force is defined as the product of mass and acceleration$.$

$\circ\sf\:F=m\times a$

$\circ\sf\:\sqrt{6^2+2^2+8^2}=m(\sqrt{3^2+2^2+4^2})$

$\circ\sf\:\sqrt{104}=m\times \sqrt{29}$

$\circ\sf\:m=\sqrt{\dfrac{104}{29}}$

$\circ\sf\:m=\sqrt{3.58}$

$\circ\:\boxed{\bf{\purple{m=1.9\:kg}}}$