Q: Two planets have masses $$M_1$$ and $$M_2$$ and radii $$R_1$$ and $$R_2. $$Which formula gives the ratio of their surface gravities?

$$g_1$$ / $$g_2$$ = ($$M_1$$ / $$M_2$$) \times ($$R_2^2$$ / $$R_1^2$$)$$

Question 1

A car of mass $$m is $$moving at constant speed $$v$$ around a flat circular track of radius $$r. $$What is the magnitude of the frictional force required to keep the car moving in a circle?

Accepted Answer

$$F = m v^2$ / r$$

Question 2

A pilot experiences a 'heavier feeling' at the bottom of a vertical loop. Which of the following best explains this sensation?

Accepted Answer

The normal force is greater than the gravitational force at the bottom of the loop.

Question 3

Which equation correctly expresses Newton's Law of Universal Gravitation?

Accepted Answer

$$F = G \frac{m_1$ m_2$}{r^2$}$$

Question 4

A satellite orbits Earth at a distance $$r$$ from the center of the planet. Which formula gives its orbital speed $$v$$?

Accepted Answer

$$v = \sqrt{G M / r}$$

Question 5

If the radius of a planet is doubled but its mass remains the same, how does the gravitational acceleration at its surface change?

Accepted Answer

It becomes one-fourth as large.

Question 6

A roller coaster car of mass $$m is at $$the top of a vertical loop of radius $$r. $$What is the minimum speed $$v$$ required so that the car does not fall off the track?

Accepted Answer

$$v = \sqrt{g r}$$

Question 7

Which of the following statements about apparent weight is correct?

Accepted Answer

Apparent weight is the normal force exerted on a body, which can differ from the true weight depending on acceleration.

Question 8

A banked curve is designed so that no friction is required for a car to make the turn at speed $$v. $$Which equation relates the banking angle $$	heta$$, speed $$v$$, and radius $$r$$?

Accepted Answer

$$	an 	heta = v^2$ / (r g)$$

Question 9

The period $$T of a $$satellite in circular orbit around a planet of mass $$M$$ and orbital radius $$r is $$given by which formula?

Accepted Answer

$$T = 2 \pi \sqrt{r^3$ / (G M)}$$

Question 10

A person is in an elevator accelerating upward with acceleration $$a. $$What is the apparent weight of the person?

Accepted Answer

$$N = m (g + a)$$

Question 11

Two planets have masses $$M_1$$ and $$M_2$$ and radii $$R_1$$ and $$R_2. $$Which formula gives the ratio of their surface gravities?

Accepted Answer

$$g_1$$ / $$g_2$$ = ($$M_1$$ / $$M_2$$) 	imes ($$R_2^2$$ / $$R_1^2$$)$$

Question 12

A person feels 'weightless' at the top of a roller coaster loop. What is the condition for this sensation?

Accepted Answer

The normal force is zero; only gravity provides the required centripetal force.

Question 13

Which of the following best describes the direction of centripetal acceleration for an object in uniform circular motion?

Accepted Answer

It is always directed toward the center of the circle.

Question 14

A geostationary satellite orbits Earth at a radius $$r. If $$Earth's mass is $$M$$, what is the formula for the gravitational force acting on the satellite?

Accepted Answer

$$F = G \frac{M m}{r^2$}$$

Question 15

A car travels around a banked curve of radius $$r at $$speed $$v. If $$the banking angle is $$	heta$$ and there is no friction, what is the relation between $$v$$, $$r$$, and $$	heta$$?

Accepted Answer

$$v = \sqrt{r g 	an 	heta}$$

Question 16

Which of the following is a correct expression for the centripetal acceleration $$a_c of an $$object moving in a circle of radius $$r at $$speed $$v$$?

Accepted Answer

$$a_c = v^2$ / r$$

Question 17

If the gravitational force between two objects is $$F$$, what will the force be if the distance between them is tripled?

Accepted Answer

It will be $$F / 9$$

Question 18

A satellite orbits a planet of mass $$M at $$radius $$r. $$Which formula gives the period $$T of $$the satellite's orbit?

Accepted Answer

$$T = 2 \pi \sqrt{r^3$ / (G M)}$$

Question 19

Which of the following is true about the gravitational force between Earth and the Moon?

Accepted Answer

It is equal in magnitude and opposite in direction for both bodies.

Dynamics of Circular Motion and Gravitation: Key Concepts and Formulas

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