Question

A \[5\text{ }kg\] mass falls through \[400\text{ }cm\]. The work done on it by the earth's gravitational force is
A) 196J
B) 1960J
C) 980J
D) 19.6J

Answer 1

Hint: The work done asked here is the scalar or magnitude of the work done when lifting the object up or down by a certain height. Hence, the work done is a product of force and height, here the force is produced by gravity as the acceleration acts upon the body. The formula for the work done is:
\[W=F.h\] with (\[F=mg\])
where \[m\] is the mass in kg, \[g\] is the gravity which is \[g=9.8m{{s}^{-2}}\], and \[h\] is the height of uplift and downfall.

Complete step by step solution:
Now to find the work done by the gravitational force, we need the force and the formula for the force is the product of mass and gravity under which the mass is influenced upon. So the force due to gravity is:
\[F=mg\]
Placing the values of mass and gravity as \[g=9.8m{{s}^{-2}}\], we get the force in N as:
\[F=5\times 9.8\]
\[=5\times 9.8\]
\[=49N\]
We now have the force required for the work done, hence, replacing the value of the force into the work done formula we get the value of the work done as:
 \[W=F.h\]
Changing the value of the height from centimeter to meters we get the value of the work done as:
\[W=49\times 4m\]
\[=196J\]
Therefore, the magnitude of the work done is given as: \[196J\].

Note: This magnitude of the work done is true for both the body raised or falling when close to the Earth’s surface where the gravity is uniform.