Question 1

A block of mass $$m is $$attached to a spring and stretched to its maximum length $$\Delta x. If $$the coefficient of friction between the block and the surface is $$\mu_k$$, what is the maximum stretch $$\Delta x of $$the spring before the block begins to slide back?

Accepted Answer

$$\mu_k m g / k$$

Question 2

According to Newton's Law of Gravitation, what is the net gravitational force $$F on an $$object of mass $$m$$ located a distance $$R$$ from the center of a uniform sphere of mass $$M ($$outside the sphere)?

Accepted Answer

$$F = \dfrac{G M m}{R^2$}$$

Question 3

How does the net gravitational force on an object of mass $$m$$ change when it is located inside a uniform sphere of mass $$M$$ compared to when it is outside?

Accepted Answer

It is less than the force outside.

Question 4

A planet has uniform density, radius $$R$$, and mass $$M_p. $$What is the expression for the partial mass $$m_p of $$the planet that contributes to the gravitational force on an object of mass $$m$$ located a distance $$r$$ from the center (where $$r \u003c R$$)?

Accepted Answer

$$m_p = \dfrac{M_p}{R^3$} r^3$

Question 5

Given the partial mass $$m_p$$ inside a planet, what is the gravitational force $$F_G(r) on an $$object of mass $$m at a $$distance $$r$$ from the center (where $$r \u003c R$$)?

Accepted Answer

$$F_G(r) = \dfrac{G M_p m}{R^3$} r$$

Question 6

Which of the following best describes the gravitational force on an object as it moves from the center of a uniform sphere to a distance $$r \u003e R$$ outside the sphere?

Accepted Answer

It increases linearly with $$r$$ inside the sphere, then decreases as $$1/r^2$$ outside.

Question 7

A large spherical shell of uniform mass contains a small object within its thickness. According to Newton's Shell Theorem, what is the net gravitational force on the object if it is located anywhere inside the shell?

Accepted Answer

Zero

Question 8

The gravitational field $$g of a $$thin spherical shell of radius $$R_0 as a $$function of distance $$r$$ from the center is given by $$g = \dfrac{G M}{r^2$}$$ for $$r \u003e R_0$. What type of object does this describe?

Accepted Answer

A thin spherical shell with negligible thickness

Question 9

A planet has twice the mass of Earth and half its radius. What is the gravitational field $$g_p at $$its surface compared to Earth's $$g$$?

Accepted Answer

$$g_p = 8g$$

Question 10

A sphere of radius $$R$$ and mass $$M is $$concentric with a thin spherical shell of radius $$3R$$ and mass $$M. $$What is the gravitational field strength at a location $$P$$ that is a distance $$2R$$ from the sphere's center?

Accepted Answer

$$g = \dfrac{G M}{(2R)^2$}$$

Question 11

A rocket of initial mass $$m is $$launched from the surface of a planet of radius $$R$$ and mass $$M. It $$reaches an orbit at a distance $$2R$$ above the planet's surface, having decreased its mass to $$\frac{1}{2}m. $$What is the gravitational field strength on the rocket in orbit?

Accepted Answer

$$g = \dfrac{G M}{9 R^2$}$$

Question 12

How does the decreasing mass of the rocket affect the gravitational field strength it experiences in orbit?

Accepted Answer

It does not affect the gravitational field strength.

Question 13

If an object is moved from position A to position B inside a spherical shell, what is the difference in the gravitational force it experiences?

Accepted Answer

There is no difference; the net force is zero everywhere inside the shell.

Question 14

Which of the following is a direct consequence of Newton's Shell Theorem?

Accepted Answer

A spherical shell exerts no net gravitational force on an object located anywhere inside it.

Question 15

A planet with uniform density has radius $$R$$ and mass $$M_p. An $$object of mass $$m is $$located at a distance $$r$$ from the center ($$r \u003c R). $$What is the gravitational field $$g(r) at $$that location?

Accepted Answer

$$g(r) = \dfrac{G M_p}{R^3$} r$$

Question 16

Which real-world scenario best illustrates the application of Newton's Law of Gravitation?

Accepted Answer

Calculating the force between Earth and a satellite in orbit.

Question 17

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

Accepted Answer

It becomes one-fourth as strong.

Question 18

A thin spherical shell of radius $$R$$ and mass $$M$$ surrounds a point mass $$m at $$its center. What is the net gravitational force on $$m$$ due to the shell?

Accepted Answer

Zero

Newton's Law of Gravitation and Gravitational Fields: Review and Applications

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