Question

An object of mass 1kg has a P.E. of 1 J relative to the ground when it is at a height of
A. 0.012m
B. 1m
C. 9.8m
D. 32m

Answer 1

Hint: Here the height of an object is asked from the ground and gravitational potential energy and mass of the object are given and with the help of the given data we can find the height. Here the value of acceleration due to gravity is taken \[9.8m/s\]. We just have to substitute the given values in the formula.

Formula used:
\[P.E.=mgh\]

Complete step-by-step solution:
The potential energy in the form of energy that is stored within an object or a substance due to its position or the arrangement of the object.
Here the potential energy given is relative to the ground that is gravitational potential energy. The gravitational potential energy is due to the force of gravity of earth which pulls us towards the ground. Hence we can say that potential energy is associated with the vertical line. Then the potential energy stored in an object which is h meters above the ground and having a mass m is given as
\[P.E.=mgh\]
Where a is acceleration due to gravity. Substituting value of \[m=1kg,\text{ }g=9.8m/s\text{ }and\text{ }P.E.=1J\]in the above equation we can find the value of h
\[\begin{align}
  & h=\dfrac{P.E.}{mg} \\
 & \Rightarrow h=\dfrac{(1J)}{(1kg)(9.8m/s)} \\
 & \Rightarrow h=0.102m \\
\end{align}\]
Hence the correct option is A.

Note: In case there were two bodies of masses M and m respectively then the gravitational potential energy is given as
\[P.E.=-\dfrac{GMm}{r}\]
Where r is the distance between the two bodies and G is the gravitational constant. The negative sign shows the loss of potential energy when work is done. Similarly, there are different- different formulas for P.E. as per there use.