Question

An object of mass $1\mathrm{kg}$ has a P.E. of $1\mathrm{J}$ relative to the ground when it is at a height of

• A. $0.102\mathrm{m}$
• B. $1\mathrm{m}$
• C. $9.8\mathrm{m}$
• D. $32\mathrm{m}$

Answer 1

The correct option is A

$0.102\mathrm{m}$

Step 1: Given data

The mass of the object,$m=1\mathrm{kg}$

The potential energy of the object, $P.E.=1\mathrm{J}$

Step 2: Calculating the height of the object

The potential energy of an object is given by

$P.E.=mgh$,

where $m$ is the mass of the object, $g$ is the acceleration due to gravity, and $h$is its height relative to the ground.

Consider $g=9.8\mathrm{m}/{\mathrm{s}}^2$

Substituting the given values, the height of the object relative to the ground is

$$\begin{gathered} 1J=1kg\times 9.8m{s}^{-2}\times hm \\ \frac{1}{9.8}=h \\ h=0.102m \end{gathered}$$

Thus, the height of the object relative to the ground is $0.102\mathrm{m}$.

Hence, option A is correct.