Gravitation and Periodic Motion

A newly discovered comet, named Comet Celestia, has orbital characteristics similar to those of Comet Halley. It travels in an elliptical orbit around the sun, visiting Earth approximately once every 80 years. Given that Comet Celestia's perihelion distance is 1.2 × 10^8 km and its aphelion distance is 6.5 × 10^9 km, calculate the length of the semi-major axis of Comet Celestia's elliptical orbit.

• 7.8 × 10^9 km
• 2.1 × 10^9 km
• 3.31 × 10^9 km

• 4.5 × 10^9 km

Comet Nebula, a newly discovered celestial wanderer, has an elliptical orbit around the sun. It pays a visit to Earth every 90 years. The perihelion distance is 1.5 × 10^8 km, and the aphelion distance is 4.2 × 10^9 km. Determine the length of the semi-major axis for Comet Nebula's elliptical orbit.

• 3.5 × 10^9 km
• 2.2 × 10^9 km

• 6.7 × 10^8 km
• 9.4 × 10^9 km

A comet named Stellaris completes one orbit around the sun every 60 years. Its perihelion distance is 9 × 10^7 km, and the aphelion distance is 5.8 × 10^9 km. Calculate the length of Stellaris's semi-major axis.

• 7.9 × 10^8 km
• 2.904 × 10^9 km
• 1.2 × 10^10 km
• 4.5 × 10^9 km

Ganymede, one of Jupiter's largest moons, orbits the planet at a distance of 10.7 astronomical units (AU) from Jupiter's center. If Io, another moon of Jupiter, is 4.2 AU away from Jupiter's center and has an orbital period of 1.8 Earth-days, predict Ganymede's orbital period in Earth-days using Kepler's third law.

• 7.320

• 3.1415
• 9.876
• 5.9366

A 2.00-kg block is attached to a spring, allowing it to move horizontally on a frictionless surface. The spring has a force constant of 196 N/m. If the block is released from a position 0.05 m away from the equilibrium position, determine the frequency (f)f the resulting oscillations in the spring-mass system.

• f≈1.45Hz

• f≈1.12Hz

• f≈2.14Hz

• f≈1.58Hz

A 1.5 kg block is attached to a spring with a force constant of 250 N/m. The block is displaced from its equilibrium position by 0.08 m and released. Calculate the angular frequency (ω) of the resulting oscillations in the spring-mass system.

• ω≈15.24rad/s

• ω≈12.92rad/s

• ω≈43.12rad/s

• ω≈17.23rad/s

A 2.5 kg block is connected to a spring with a force constant of 180 N/m. If the block is displaced by 0.1 m from its equilibrium position and released, find the period (T) of the resulting oscillations.

• 0.74s

• 0.31s

• 2.51s

• 1.25s

A student conducts a physics experiment using a simple pendulum with a length of 50.0 cm. The measured frequency of oscillation is 1.20 Hz. Calculate the gravitational acceleration at the location of the experiment.

• 5.00 m/s²
• 1.20 m/s²
• 15.00 m/s²
• 9.81 m/s²

A block with a mass of 1.5 kg is attached to a spring with a force constant of 250 N/m. If the block is displaced by 0.08 m from its equilibrium position and released, what is the angular frequency (ω) of the resulting oscillations in the spring-mass system?

• 12.92 rad/s

• 2.50 rad/s

• 125.00 rad/s

• 0.08 rad/s

Comet Celestia has an elliptical orbit around the sun, with a perihelion distance of 1.2 × 10^8 km and an aphelion distance of 6.5 × 10^9 km. Calculate the length of the semi-major axis of Comet Celestia's orbit.

• 4.5 × 10^9 km

• 2.8 × 10^9 km

• 7.2 × 10^9 km

• 3.31 × 10^9 km