A planet moves around the sun. At a point $P$ at a distance $d_{1}$ , the planet has a speed $v_{1}$ . At another point $Q$ at a distance $d_{2}$ , its speed will be

d_{1}^{2} v_{1} / d_{2}^{2}

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d_{2} v_{1} / d_{1}

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d_{1} v_{1} / d_{2}

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d_{2}^{2} v_{1} / d_{1}^{2}

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Solution

The correct option is C $d_{1} v_{1} / d_{2}$
In planetary motion ${¯ t}_{e x t} . = 0 \Rightarrow ¯ L = c o n s t a n t$
$¯ L = ¯ r \times ¯ p (= m ¯ v) = m r v (∵ θ = 90^{\circ})$
So $m_{1} d_{1} v_{1} = m_{2} d_{2} v_{2}$ (here $r = d$ )
$\to v_{2} = \frac{v_{1} d_{1}}{d_{2}}$

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A planet moves around the sun. At a point $P$ at a distance $d_{1}$ , the planet has a speed $v_{1}$ . At another point $Q$ at a distance $d_{2}$ , its speed will be

The correct option is C $d_{1} v_{1} / d_{2}$
In planetary motion ${¯ t}_{e x t} . = 0 \Rightarrow ¯ L = c o n s t a n t$
$¯ L = ¯ r \times ¯ p (= m ¯ v) = m r v (∵ θ = 90^{\circ})$
So $m_{1} d_{1} v_{1} = m_{2} d_{2} v_{2}$ (here $r = d$ )
$\to v_{2} = \frac{v_{1} d_{1}}{d_{2}}$