A planet moves around the sun. At a given point P, it is closed from the sun at a distance d1 and has a speed v1. At another point Q. when it is farthest from the sun at a distance d2, its speed will be

Question

A planet moves around the sun. At a given point P, it is closed from the sun at a distance d1 and has a speed v1. At another point Q. when it is farthest from the sun at a distance d2, its speed will be (A) (d21v1/d22) (B) (d2v1/d1) (C) (d1 v1/d2) (D) (d22 v1/d21)

Tardigrade Admin · Accepted Answer

According to law of conservation of angular momentum mv1d1 = mv2d2 mv1d1 = mv2d2 ∴ v2 = (d1v1/d2)

Q. A planet moves around the sun. At a given point $P$ , it is closed from the sun at a distance $d_{1}$ and has a speed $v_{1}$ . At another point $Q$ . when it is farthest from the sun at a distance $d_{2}$ , its speed will be

$\frac{d _{1}^{2} v _{1}}{d _{2}^{2}}$

$\frac{d _{2} v _{1}}{d _{1}}$

$\frac{d _{1} v _{1}}{d _{2}}$

$\frac{d _{2}^{2} v _{1}}{d _{1}^{2}}$

According to law of conservation of angular momentum

$m v_{1} d_{1} = m v_{2} d_{2}$

$m v_{1} d_{1} = m v_{2} d_{2}$

$∴ v_{2} = \frac{d _{1} v _{1}}{d _{2}}$

Q. A planet moves around the sun. At a given point P, it is closed from the sun at a distance d1​ and has a speed v1​. At another point Q. when it is farthest from the sun at a distance d2​, its speed will be

d22​d12​v1​​

d1​d2​v1​​

d2​d1​v1​​

d12​d22​v1​​