Question

A woman weighing \[63\]kg eats plum cake whose energy content is \[9800\] calories. If all this energy could be utilized by her, she can ascend a height of:
(A) \[1\]m
(B) \[66\]m
(C) \[100\]m
(D) \[42\]m

Answer 1

Hint:This given problem can be seen as an example of gravitational potential energy. The potential energy of a body can be defined as the energy possessed by the body by means of its position or configuration in some field.

Step-by-step solution:
Step 1: Gravitational potential energy of a body can be defined as the energy possessed by the body by means of its position above the surface of earth.
In fact, the amount of work done in carrying a body from the surface of earth to its present position against the gravitational force of earth, is stored in the body in the form of its gravitational potential energy. When the same body is allowed to fall back from its position, the work will be done in the same amount of stored potential energy. We know that the gravitational potential energy can be calculated by taking the consideration of force applied on the body to overcome the gravitational attraction when the body is lifted from the surface at some height or it falls back from the same given height.
So, let us say that the mass of the body is \[ = m\], acceleration due to gravity on the surface of earth is \[ = g\], and height through which the body is raised (or falls back) is \[ = h\].
So, work done = force x distance
\[W = mgh\]
This work done will be stored as energy so,
\[mgh = 9800\]calories
And 1 calorie = 4.18J
So, \[mgh = 9800 \times 4.18\] ……………..(1)
Form the given question \[m = \]63kg, \[g = \]9.8m/s², and \[h = \]?
So, keeping the values in above equation –
\[mgh = 9800 \times 4.18\]
\[h = \dfrac{{9800 \times 4.18}}{{63 \times 9.8}}\]
\[h = 66.34\]m

So, the correct option is (B).

Note:
-It should be remembered that when height is not too large then the value of \[g\] is practically constant but if height is too large then the value of \[g\] will be varied and it will depend on height.