Question

Do the circled question i.e. 6 and 8

Refer to the attachment, Thank you!

(You can skip Graph question If graph ain't available) ​

Answer 1

6. 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) 0 units (ii) 2 units

Sol: Assume that the distance travelled be x and work done be y.

Work done by body is directly proportional to distance travelled. So,

y ∝ x

If we remove the sign of proporinalty then there comes a constant k. So, y = kx.

(force = k = 5 units)

→ y = 5x

Now, take value of x = 0, 1, -1. On solving we get,

y = 0, 5, -5

(Plot the graph taking x as 0, 1, -1 and y as 0, 5, -5)

(i) 2 units

Means x = 2

y = 5(2) = 10

So, work done is 10 units

(ii) 0 units (x = 0)

y = 5(0) = 0 units

Work done is 0 units

7. In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius: F = (9/5)C + 32

(i) Draw the graph of the linear equation above using Celsius for x-axis and Fahrenheit for y-axis.

(ii) If the temperature is 30°C, what is the temperature in Fahrenheit?

(iii) If the temperature is 95°F, what is the temperature in Celsius?

(iv) If the temperature is 0°C, what is the temperature in Fahrenheit and if the temperature is 0°F, what is the temperature in Celsius?

(v) Is there a temperature which is numerically the same in both Fahrenheit and Celsius? If yes, find it.

Sol: (i)Given that, F = (9/5)C + 32

Now, first take F as 0 then C as 0.

→ 0 = (9/5)C + 32 [ F as 0 ]

→ -9/5 C = 32

→ C = 32 × -5/9

→ C = -17.78

→ F = (9/5)(0) + 32 [ C as 0 ]

→ F = 32

(ii) If temperature is 30°C then,

→ F = (9/5)C + 32

→ 5F - 9C = 160 ..............(1st equation)

→ 5F - 9C = 160

→ 5F - 9(30) = 160

→ 5F - 270 = 160

→ 5F = 430

→ F = 86°F

(iii) If temperature is 95° F then,

 → 5F - 9C = 160

→ 5(95)- 9C = 160

→ 475 - 9C = 160

→ 315 = 9C

→ C = 35°

(iv) If temperature is 0°C then,

→ 5F - 9(0) = 160

→ 5F = 160

→ F = 32°F

 If the temperature is 0°F then,

→ 5(0) - 9C = 160

→ -9C = 160

→ C = -17.8°C

(v) Yes, for this we have to take both temperature same or equal i.e. C = F

→ 5F - 9C = 160

→ 5F - 9F = 160

→ -4F= 160

→ F = -40

Therefore, F = C = -40°