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NEET 2009
Exam
NEET
Year
2009
Subject
Physics
Chapter
Gravitation

NEET 2009 · Physics · Gravitation

The figure shows elliptical orbit of a planet m about the sun S ....

The figure shows elliptical orbit of a planet mm about the sun S\mathrm{S}. The shaded area SCD is twice the shaded are SAB\mathrm{SAB}. It t1t_1 is the time for the planet to move from CC to DD and t2t_2 is the time to move from AA to BB then The figure shows elliptical orbit of a planet m about the sun S . The shaded area SCD is twice the shaded are SAB . It

Options

  1. At1=t2\mathrm{t}_1=\mathrm{t}_2
  2. Bt1>t2t_1>t_2
  3. Ct1=4t2t_1=4 t_2
  4. Dt1=2t2t_1=2 t_2

Correct answer

D. t1=2t2t_1=2 t_2

Step-by-step solution

Kepler's 2nd 2^{\text{nd }} law⇒(ΔAΔt)planet = constant A1t1=A2t2⇒2 At1=At2⇒t1=2t2\begin{aligned}& \Rightarrow\left(\frac{\Delta \mathrm{A}}{\Delta \mathrm{t}}\right)_{\text{planet }}=\text{ constant }\\ & \frac{\mathrm{A}_1}{\mathrm{t}_1}=\frac{A_2}{t_2}\\ & \Rightarrow \frac{2 \mathrm{~A}}{\mathrm{t}_1}=\frac{A}{t_2}\\ & \Rightarrow \mathrm{t}_{1}=2 \mathrm{t}_{2} \end{aligned}
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