Kepler’s Law of Planetary Motion NEET Questions

Kepler’s Law of Planetary Motion

Kepler’s Law of Planetary Motion MCQ Questions

7.
Which of the following correctly describes the eccentricity of an ellipse?
A.
e = 0 for a circle, 0 < e < 1 for an ellipse, e = 1 for a parabola
B.
e = 1 for a circle, 0 < e < 1 for an ellipse
C.
e > 1 for all ellipses
D.
e = 0 for all planetary orbits (they are perfect circles)
ANSWER :
A. e = 0 for a circle, 0 < e < 1 for an ellipse, e = 1 for a parabola
8.
Kepler's Second Law (Law of Areas) states that:
A.
A planet moves faster when farther from the Sun and slower when nearer
B.
The line joining a planet to the Sun sweeps equal areas in equal intervals of time
C.
The orbital speed of a planet is proportional to its distance from the Sun
D.
The area swept is proportional to the square of the time interval
ANSWER :
B. The line joining a planet to the Sun sweeps equal areas in equal intervals of time
9.
The Law of Areas (Kepler's Second Law) is a consequence of:
A.
Newton's third law of motion
B.
Conservation of kinetic energy
C.
Conservation of angular momentum for any central force
D.
Conservation of linear momentum
ANSWER :
C. Conservation of angular momentum for any central force
10.
Using the Law of Areas, if r_P and v_P are the distance and speed at perihelion, and r_A and v_A at aphelion, the relation between them is:
A.
v_P / v_A = r_A / r_P (since L = mr·v is conserved when r ⊥ v at apsides)
B.
v_P / v_A = r_P / r_A
C.
v_P × r_P² = v_A × r_A²
D.
v_P = v_A (speed is constant throughout orbit)
ANSWER :
A. v_P / v_A = r_A / r_P (since L = mr·v is conserved when r ⊥ v at apsides)
11.
A planet at perihelion (closest point) has speed v_P and distance r_P from the Sun. At the aphelion r_A = 3r_P. The speed at aphelion is:
A.
v_A = v_P/3
B.
v_A = 3v_P
C.
v_A = v_P/9
D.
v_A = v_P√3
ANSWER :
A. v_A = v_P/3
12.
A comet has maximum speed v₁ at perihelion (distance r₁) and minimum speed v₂ at aphelion (distance r₂). The areal velocity of the comet is:
A.
½r₁v₁ = ½r₂v₂ = constant = L/(2m)
B.
r₁v₁² = r₂v₂²
C.
r₁²v₁ = r₂²v₂
D.
r₁v₁ + r₂v₂ = constant
ANSWER :
A. ½r₁v₁ = ½r₂v₂ = constant = L/(2m)