Question

A particle of mass 100g is thrown vertically upwards with a speed of 5m/s. The work done by the force of gravity during the time the particle goes up is
${\text{A}}{\text{. }} - 0.5J \\\ {\text{B}}{\text{. }} - 12.5J \\\ {\text{C}}{\text{. }} - 1.25J \\\ {\text{D}}{\text{. }}0.5J \\\$

Answer 1

Hint : The work done by any force is equal to the product of force and the distance travelled by the object on which the force is applied. The gravitational force is equal to the product of mass of the body and the acceleration due to gravity while the displacement of the particle can be found by using one of the equations of motion.
Formula used:
The work done on a body is given as
$W = FS\cos \theta$
Here F is the force acting on the object while S is the displacement produced in the object and $\theta$ is the angle between force and displacement of particle.
The gravitational force on an object can be given as
$F = mg$
Here m is the mass of the object while g is the acceleration due to gravity whose value we will take to be
$g = 10m/{s^2}$
There are three equations of motion which can be used for describing motion of the particle. They are given as
$\begin{gathered} v = u + at \\\ {v^2} - {u^2} = 2aS \\\ S = ut + \dfrac{1}{2}a{t^2} \\\ \end{gathered}$
Here the symbols have their usual meanings.

Detailed step by step solution:
We are given a particle whose mass is given as
$m = 100g = 0.1kg$
The particle is thrown upwards with an initial velocity which is given as
$u = 5m/s$
We need to find the work done by the gravitational force on the object only during the upward journey. The final velocity at the highest point is equal to zero.
$v = 0$
We can use the second equation of motion to calculate the distance travelled by the object as it goes upward in the gravity.
${v^2} - {u^2} = 2aS \\\ 0 - {\left( 5 \right)^2} = 2 \times \left( { - 10} \right) \times S \\\ \- 25 = - 20S \\\ S = \dfrac{{25}}{{20}} = \dfrac{5}{4} = 1.25m \\\$
The gravitational force on the object is given as
$F = mg = 0.1 \times 10 = 1N$
Hence the work done is given as
$W = FS\cos 180^\circ \\\ = - 1 \times 1.25 = - 1.25J \\\$

The angle between force and displacement is equal to $180^\circ$ since they are directed in opposite directions. The correct answer is option C.

Note: 1. Don’t forget to keep all quantities in the same system of units preferably the SI system of units.
2. Since the body decelerates when thrown upwards under the influence of gravity, we have taken the value of g to be negative.