Question

The Earth moves round the Sun in an elliptical orbit as shown in figure.

The ratio $\frac{OA}{OB}=x$, the ratio of the speed of the earth at B and at A is nearly

• A. $\sqrt{x}$
• B. $x$
• C. $x\sqrt{x}$
• D. $x^2$

Answer 1

The correct option is B

$x$

Since there is no external force acting, therefore, the torque developed would be 0 and hence angular momentum would be conserved. So, applying conservation of ANGULAR momentum at point A and B.

Initial angular momentum $=OA\times m{v}_A=OA\left(m{v}_A\right)$

Final angular momentum $=OB\times m{v}_B=OA\left(m{v}_B\right)$

So, $OA\left(m{v}_A\right)=OB\left(m{v}_B\right),\frac{v_A}{v_B}=\frac{1}{x}or\frac{v_B}{v_A}=x$