Science|Math|Engineering
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
$\displaystyle \frac{dA}{dt} = constant$
$\displaystyle \frac{A_1}{2} = \frac{A_2}{3} = \frac{A_3}{6} $
On multiplying by 6 ,
A1 = 2A2 = A3
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
Q: In the solar system, which is conserved
(a) total energy
(b) K.E.
(c) angular velocity
(d) linear momentum
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}} $
$\displaystyle L = m \sqrt{\frac{G M}{R_0} } \; R_0$
$\displaystyle L = \sqrt{G M R_0}$
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 $