Question

A bag of wheat weighs $100$ kilograms. To what height should it be raised so that its potential energy may be \[9800\,J\] (\[g = 9.8\,m{s^{ - 2}}\]) ?
A. \[2\]
B. \[100\]
C. \[50\]
D. \[0\]

Answer 1

Hint:This question is from the topic of work, energy, and power. The concept of potential energy, especially gravitational potential energy, is used to solve this question. Here the gravitational potential energy represents the potential an object has to do work due to being located at a particular position in a gravitational field.

Complete step by step answer:
The mass of the weight bag, \[m = 100\,kg\]
The value of gravity, \[g = 9.8\,m{s^{ - 2}}\]
The potential energy stored in the object when it is raised to a certain height is given by:
\[P = mgh\]
We are considering the potential energy at the ground level to be zero.

Now, let us assume the height to be \[h\]. Now, the potential energy is given by
\[ \Rightarrow P = mgh\]
Now, we put the values of known quantities,
\[ \Rightarrow 9800 = 100 \times 9.8 \times h\]
Doing the calculations and isolating the variable in the equation, h from the other parameters such as the constants, we get,
\[ \Rightarrow 9800 = 980 \times h\]
After, calculating we get,
\[ \therefore h = 10\,m\]

Thus, option C is the correct answer.

Note:We must keep the unit conversions in mind and change the units so that every physical quantity is in its SI unit before solving any numerical. The formula for potential energy \[P = mgh\] gives us the change in potential energy and not the absolute potential. We always take a reference point to measure the potential energy relatively. The most general reference is the potential energy at ground level is considered as zero.