Question

A bag of rice weighs $200$ kg. To what height should it be raised, so that its potential energy may become $9800\,J?$ (Take $g = 9.8\,m{s^{ - 2}})$
A. $2.5,m$
B. $5\,m$
C. $10\,m$
D. $9.8\,m$

Answer 1

Hint: Potential energy of the body can be defined as the energy which is possessed by the virtue of the position or the height of the object. Here we will use the standard formula for the potential energy which is the product of mass, acceleration due to gravity and the height of the object and will simplify for the required value.

Complete step by step answer:
Given that: mass, m $ = 200kg$, acceleration due to gravity, $g = 9.8m/{s^2}$, potential energy, P.E.$ = 9800J$, height, $h = ?$.
Potential energy can be given by using the formula,
P.E.$ = mgh$
Place the given values in the above expression –
$9800 = 200 \times 9.8 \times h$
Make the required term “h” the subject and move other terms on the opposite side. Term multiplicative on one side if moved to the opposite side then it goes in the denominator.
$\dfrac{{9800}}{{200 \times 9.8}} = h$

The above equation can be re-written as –
$h = \dfrac{{9800}}{{200 \times 9.8}}$
Find the factors of the term on the numerator and the denominator and also remove decimal points.
$h = \dfrac{{98 \times 100 \times 10}}{{2 \times 100 \times 98}}$
Common factors from the numerator and the denominator cancel each other and therefore remove and from the numerator and the denominator.
$h = \dfrac{{10}}{2}$
Simplify finding the division of the above expression –
$ \therefore h = 5\,m$

Hence, option B is correct.

Note: Always remember the difference between the types of energy and the standard equation for it since it is the main and important factor for the solution. Always put the appropriate unit once the solution is done and also all the units should be in the same system of units while placing in the standard formula.