Question

To verify Kepler's third law graphically four students plotted graphs. Student A plotted a graph of T (period of revolution of planets) versus r (average distance of planets from the sun) and found the plot is straight line with slope 1.85. Student B plotted a graph of T² v/s r³ and found the plot is straight line with slope 1.39 and negative Y-intercept. Student C plotted graph of log T v/s log r and found the plot is straight line with slope 1.5. Student D plotted graph of log T v/s log r and found the plot is straight line with slope 0.67 and with negative X-intercept. The correct graph is of student

Options

• A

• B

• C

• D

Answer 1

C

Explanation:

Plot of T vs r is not a straight line. Plot of T² v/s r³ is a straight line graph passing through origin.

According to Kepler's third law,

T² = Kr³, where K is constant of proportionality.

Taking log, 2 log T = log K + 3 log r

∴ log T = `log K/2 + 3/2 log r`

Comparing with y = mx + c,

m = `3/2` = 1.5

As a result, the graph of log T v/s log r is a straight line with a slope of 1.5.