Question

At this instant, the planet Xenor rotates about its sun once every 3.91 Earth years. Because of the presence of an asteroid belt, Xenor’s motion about its sun is slowing; it experiences an angular acceleration of −7.72 × 10−21 rad / s2. How many Xenor years will it be before one Xenor year corresponds to four Earth years? Note that the Xenor year is lengthening as time passes. Select one: a. 2.97 × 101 years b. 1.19 × 103 years c. 1.26 × 103 years d. 7.48 × 103 years

Answer 1

Initial angular velocity of Xenor, w0 = 2pi / (3.91 x 365 x 24 x 60 x 60) rad/s

= 5.095 x 10^-8 rad/s

Final angular velocity of Xenor. w = 2pi / (4.0 x 365 x 24 x 60 x 60) rad/s

= 4.98 x 10^-8 rad/s

Acceleration, a = -7.72 x 10^-21 rad/s^2

Suppose, t is the time required to achieve the angular velocity w.

Use the expression -

w = w0 + a*t

=> 4.98 x 10^-8 = 5.095 x 10^-8 + (-7.72 x 10^-21 * t)

=> t = (4.98 - 5.095) x 10^-8 / (-7.72 x 10^-21) = (0.115 x 10^-8) / (7.72 x 10^-21) = 0.0149 x 10^13 s

Convert this in years.

t = (0.0149 x 10^13) / (365 x 24 x 60 x 60) = 7.46 x 10^3 years.

Hence, option (d) is the correct answer.