Question

The object of mass of 1 kg has a potential energy of 1 joule relative to the ground, when it is at a height of:

• A. 0.102 m
• B. 1 m
• C. 9.8 m
• D. 32 m

Answer 1

The correct option is A

0.102 m

Step 1: Given data

Mass of the body ($m$) = $1Kg$

Potential energy ($E$) = $1Joule$

Acceleration due to gravity ($g$)= $9.8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right.$

Step 2: Formula used

Potential energy is the energy that a body possesses due to the virtue of position.

The formula for potential energy

$P.E=mgh$

$m$is the mass of the object, $g$ is the acceleration due to gravity, and $h$ is the height to which the object is raised

Step 3: Calculation for potential energy

$$\begin{gathered} P.E=mgh \\ \Rightarrow P.E=1kgx9.8\frac{m}{se{c}^2}\times hmeters \\ \Rightarrow P.E=1x9.8xh \\ \Rightarrow P.E=9.8xh \\ Substituting,[PotentialEnergy=1joule.] \\ \Rightarrow 1=9.8xh \\ \Rightarrow h=\frac{1}{9.8} \\ \Rightarrow h=\frac{10}{98} \\ \Rightarrow h=0.102m \end{gathered}$$

So, the height at which potential energy is$1J$ is $0.102m.$

Hence, the correct option is A.