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Question

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


A
d21v1/d22
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B
d2v1/d1
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C
d1v1/d2
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D
d22v1/d21
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Solution

The correct option is C $$\displaystyle d_{1} v_1 / d_{2}$$
In planetary motion $$\displaystyle \bar{t}_{ext}. =0 \Rightarrow \bar{L}= constant$$
$$\displaystyle \bar{L}=\bar{r} \times \bar{p}(=m\bar{v})=mrv \ ( \because \theta=90^{\circ})$$
So $$\displaystyle m_1 d_1 v_1=m_2d_2v_2$$ (here $$\displaystyle r=d$$)
$$\displaystyle \rightarrow v_2=\frac {v_1d_1}{d_2}$$

Physics

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