Question

A certain particle has a weight of $\mathbf{22}\mathbf{}\mathit{N}$at a point where. localid="1656143387519" $\mathit{g}\mathbf{}\mathbf{=}\mathbf{}\mathbf{9}\mathbf{.}\mathbf{8}\mathbf{}\mathit{m}\mathbf{/}\mathit{s}{\mathbf{}}^{\mathbf{2}}$What are its:(a) weight and (b) mass at a point where ^{localid="1656143411696" $\mathit{g}\mathbf{}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{9}\mathbf{}\mathit{m}\mathbf{/}\mathit{s}{\mathbf{}}^{\mathbf{2}}$}? What are its (c) weight and(d) mass if it is moved to a point in space where $\mathit{g}\mathbf{=}\mathbf{0}$?

Short answer

$When,g=4.9m/s^{2}weightis11N$

$when,g=4.9m/s{}^{2}massis2.2kg$

$$\begin{gathered} when,g=0,weightis0N \\ When,g=0,massis2.2kg \end{gathered}$$

Step-by-step solution

Given information

It is given that,

$W=22N$

Determining the concept

This problem can be solved using the concept of weight and mass.

According to the concept of weight and mass,

$$\begin{gathered} W=m\times a \\ Whereaistheaccelerationduetogravity \end{gathered}$$

(a) Determining the weight when g=4.9 m/s2

As

$W=22N$

$$\begin{gathered} mass\left(m\right)=\frac{22}{9.8} \\ =2.2\mathrm{kg} \\ When,g=4.9m/s{}^2 \\ W=2.2\times 4.9 \\ =11N \end{gathered}$$

Hence, the weight when$g=4.9m/s{}^{2}is11N$

(b) Determining the mass when g=4.9 m/s2

As mass is a fundamental quantity, it will be the same anywhere,

$m=2.2kg$

Hence, the mass when $g=4.9m/s{}^{2}is2.2kg$

(c) Determining the weight when g=0 m/s2

when

$$\begin{gathered} g=0m/s{}^2 \\ W=2.2\times 0 \\ =0N \\ Hence,theweightwheng=m/s{}^{2}is0N \end{gathered}$$

(d) Determining the mass when g=0 m/s2

Mass of the body is the same irrespective of the gravitational acceleration. So, it would have the same mass as before.

$$\begin{gathered} m=2.2kg \\ Hence,themasswheng=0m/s{}^{2}is2.2kg \end{gathered}$$