If the work done by a body on application of a constant force is directly proportional to the distance travelled by the body, express this in the form of an equation in two variables and draw the graph of the same by taking the constant force as 5 units. Also read from the graph the work done when the distance travelled by the body is
(i) 2 units (ii) 0 units
Solution:
We can consider distance traveled by the body and the work done as 'x' and 'y' respectively and then apply the direct proportion property.
- Let the distance traveled and the work done by the body be x and y respectively.
- The constant force applied to the body is 5 units.
- Work done ∝ distance traveled.
Hence, y ∝ x
y = kx --- Equation (1)
Where k is the constant force applied on the body, given as 5. Thus, y = 5x.
By substituting different values of x in equation (1) we get different values for y
- When x = 0, y = 0
- When x = 1, y = 5
- When x = 2, y = 10
Thus, we have the following table with all the obtained solutions:
x |
0 |
1 |
2 |
y |
0 |
5 |
10 |
The graph of the line represented by the given equation is shown below.
(i) From the graphs, it can be observed that the value of y corresponding to x = 2 is 10 units. This implies that the work done by the body is 10 units when the distance traveled by it is 2 units.
(ii) From the graphs, it can be observed that the value of y corresponding to x = 0 is 0. This implies that the work done by the body is 0 units when the distance traveled by it is 0 units.
Video Solution:
If the work done by a body on application of a constant force is directly proportional to the distance travelled by the body, express this in the form of an equation in two variables and draw the graph of the same by taking the constant force as 5 units. Also read from the graph the work done when the distance travelled by the body is (i) 2 units (ii) 0 units
NCERT Solutions Class 9 Maths - Chapter 4 Exercise 4.3 Question 6:
Summary:
If the work done by a body on application of a constant force is directly proportional to the distance travelled by the body, then the equation in the form of two variables is given by y = kx, and the work done by travelling 2 units and 0 units distance are (i) 10 units and (ii) 0 units respectively.