Question 11 Mark
In the following Questions, the Assertion and Reason have been put forward. Read the statements carefully and choose the correct alternative from the following:
Reason: The slope of a $v-t$ graph with $60^\circ$ inclination is greater than $30^\circ$ inclination.
- Both the Assertion and the Reason are correct and the Reason is the correct explanation of the Assertion.
- The Assertion and the Reason are correct but the Reason is not the correct explanation of the Assertion.
- Assertion is true but the Reason is false.
- The statement of the Assertion is false but the Reason is true.
Reason: The slope of a $v-t$ graph with $60^\circ$ inclination is greater than $30^\circ$ inclination.
Answer
View full question & answer→The slope of the distance$–$time graph gives the speed of the object.For the particale $A$, the slope of the line is $\tan\theta_1=\tan30=\frac{1}{\sqrt{3}}$
For the particale $B,$ the slope of the line is $\tan\theta_2=\tan60=\sqrt{3}$
Thus, ratio of the velocities, $\frac{\text{V}_{\text{A}}}{\text{V}_{\text{B}}}=\frac{\tan30}{\tan60}=\frac{\frac{1}{\sqrt{3}}}{\sqrt{3}}=\frac{1}3{}$
For the particale $B,$ the slope of the line is $\tan\theta_2=\tan60=\sqrt{3}$
Thus, ratio of the velocities, $\frac{\text{V}_{\text{A}}}{\text{V}_{\text{B}}}=\frac{\tan30}{\tan60}=\frac{\frac{1}{\sqrt{3}}}{\sqrt{3}}=\frac{1}3{}$