## A planet moving around sun sweeps area A1 in 2 days, A2 in 3 days and A3 in 6 days. Then the relation between A1, A2 and A3 is

Q: A planet moving around sun sweeps area A1 in 2 days, A2 in 3 days and A3 in 6 days. Then the relation between A1, A2 and A3 is (a) 3A1 = 2A2 = A3

(b) 2A1 = 3A2 = 6A3

(c) 3A1 = 2A2 = 6A3

(d) 6A1 = 3A2 = 2A3

Ans: (a)
Sol: From Kepler’s 2nd Law (Law of Area )

$\displaystyle \frac{dA}{dt} = constant$

$\displaystyle \frac{A_1}{2} = \frac{A_2}{3} = \frac{A_3}{6}$

On multiplying by 6 ,

A1 = 2A2 = A3

## The orbital angular momentum of a satellite revolving at a distance r from the center is L . If the distance is increase to 16r , then the new angular momentum will be

Q: The orbital angular momentum of a satellite revolving at a distance r from the center is L . If the distance is increase to 16r , then the new angular momentum will be

(a) 16 L

(b) 64 L

(c) L/4

(d) 4 L

Ans: (d)

## In the solar system, which is conserved

Q: In the solar system, which is conserved

(a) total energy

(b) K.E.

(c) angular velocity

(d) linear momentum

Ans: (a)

## A satellite of mass m is circulating around the earth with constant angular velocity. If radius of the orbit is R0 and mass of the earth M , the angular momentum about the center of the earth is

Q: A satellite of mass m is circulating around the earth with constant angular velocity. If radius of the orbit is R0 and mass of the earth M , the angular momentum about the center of the earth is

(a) $m \sqrt{G M R_0}$

(b) $m \sqrt{G m R_0}$

(c) $m \sqrt{\frac{G M}{R_0}}$

(d) $M \sqrt{\frac{G m}{R_0}}$

Ans: (a)
Sol: L = m v r

$\displaystyle L = m \sqrt{\frac{G M}{R_0} } \; R_0$

$\displaystyle L = \sqrt{G M R_0}$

## In planetary motion, the angular momentum conservation leads to the law of

Q: In planetary motion, the angular momentum conservation leads to the law of

(a) Orbits

(b) Areas

(c) Periods

(d) Conservation of kinetic energy

$\displaystyle \frac{dA}{dt} = \frac{L}{2 m} = constant$