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
B
d2v1/d1
C
d1v1/d2
D
d22v1/d21

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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