Question

Superman is going on a vacation to his home planet krypton from earth via. Sun. (Let's assume for a moment that Krypton is not destroyed). His energy v/s distance travelled graph is as shown below:

At which point is superman's (dE/ds) positive?

• A. 100 million kms
• B. 150 million kms
• C. 200 million kms
• D. 1000 million kms

Answer 1

The correct option is A

100 million kms

So what we know, (dE/ds) is graphically the slope of E vs s graph. The slope at a point is given by $\tan \theta$, where $\theta$ is the angle made by the tangent at the point with x-axis. Let's see in the graph :

At 100 million km mark the angle made by tangent is ${\theta }_1$, which is acute.
= tan $\theta$1 = positive
At 150 million km the tangent is parallel to the x-axis.
Angle = 0
= tan $\theta$ = 0
Same is true for 1000 million km
At 200 million km ,
${\theta }_3$ is obtuse $\Rightarrow \tan {\theta }_3=-ve$
(since $\tan$ is $-ve$ in 2nd quadrant)