Grade 11 : Physics - Gravitation (Set 4)

Question 1

Two satellites, Satellite A and Satellite B, move around a planet in concentric circular orbits. The orbital radius of Satellite A is $R$, while the orbital radius of Satellite B is $4R$.

What is the ratio of the orbital time period of Satellite B to that of Satellite A ($T_B / T_A$)?

Accepted Answer

C) 8

Answer

A) 2

Answer

B) 4

Answer

D) 16

Question 2

A research probe is elevated vertically from the Earth's surface to a height equal to the Earth's radius $R$.

If $g$ is the acceleration due to gravity at the surface of the Earth, what is the acceleration due to gravity at this height?

Accepted Answer

B) $g/4$

Answer

A) $g/2$

Answer

C) $g/8$

Answer

D) $g/16$

Question 3

A shaft is bored straight towards the center of the Earth down to a depth equal to half of the Earth's radius ($d = R/2$).

What is the acceleration due to gravity at this depth in terms of the surface gravity $g$?

Accepted Answer

A) $g/2$

Answer

B) $g/4$

Answer

C) $3g/4$

Answer

D) $g/3$

Question 4

Consider a hypothetical planet with twice the mass of Earth ($M' = 2M$) and half the radius of Earth ($R' = R/2$).

If $v_e$ is the escape velocity from the surface of Earth, what is the escape velocity $v_e'$ from the surface of this hypothetical planet?

Accepted Answer

D) $2v_e$

Answer

A) $v_e$

Answer

B) $\sqrt{2}v_e$

Answer

C) $\sqrt{8}v_e$

Question 5

A weather satellite is placed in a circular orbit around Earth at an altitude of $h = 3R$ above the surface, where $R$ is the radius of the Earth.

What is the orbital speed of the satellite in terms of $G$, Earth's mass $M$, and Earth's radius $R$?

Accepted Answer

B) $\frac{1}{2}\sqrt{\frac{GM}{R}}$

Answer

A) $\sqrt{\frac{GM}{R}}$

Answer

C) $\frac{1}{3}\sqrt{\frac{GM}{R}}$

Answer

D) $\frac{1}{4}\sqrt{\frac{GM}{R}}$

Question 6

What is the total mechanical energy of a satellite of mass $m$ orbiting a planet of mass $M$ in a circular orbit of radius $r$?

Accepted Answer

C) $-\frac{GMm}{2r}$

Answer

A) $-\frac{GMm}{r}$

Answer

B) $\frac{GMm}{2r}$

Answer

D) $-\frac{2GMm}{r}$

Question 7

Two point masses $m_1 = M$ and $m_2 = 4M$ are fixed at a distance $D$ apart in space.

At what distance from mass $M$ along the line joining them is the net gravitational field intensity equal to zero?

Accepted Answer

B) $D/3$

Answer

A) $D/2$

Answer

C) $D/4$

Answer

D) $2D/3$

Question 8

Planet	Mass (in $M_E$)	Radius (in $R_E$)
Planet X	2	1
Planet Y	4	2

Using the data provided in the table, determine the ratio of the gravitational acceleration on Planet X to that on Planet Y ($g_X / g_Y$).

Accepted Answer

A) $2 : 1$

Answer

B) $1 : 1$

Answer

C) $4 : 1$

Answer

D) $1 : 2$

Question 9

A straight tunnel is drilled completely through the center of a uniform solid Earth of mass $M$ and radius $R$. A particle is released from rest at one end of the tunnel.

Assuming no friction, what is the period of Simple Harmonic Motion (SHM) performed by the particle inside the tunnel?

Accepted Answer

B) $2\pi \sqrt{\frac{R}{g}}$

Answer

A) $\pi \sqrt{\frac{R}{g}}$

Answer

C) $2\pi \sqrt{\frac{2R}{g}}$

Answer

D) $4\pi \sqrt{\frac{R}{g}}$

Question 10

A comet moves around the Sun in an elliptical orbit. Its distance at perihelion (closest approach) is $r_1 = r$ and at aphelion (farthest distance) is $r_2 = 3r$.

What is the ratio of the linear speed of the comet at perihelion ($v_1$) to its linear speed at aphelion ($v_2$)?

Accepted Answer

C) $3 : 1$

Answer

A) $1 : 3$

Answer

B) $1 : 9$

Answer

D) $9 : 1$

Question 11

How much work must be done by an external agent to raise a mass $m$ slowly from the surface of Earth (radius $R$) to a height $h = 2R$?

Accepted Answer

C) $\frac{2}{3} mgR$

Answer

A) $2 mgR$

Answer

B) $\frac{1}{2} mgR$

Answer

D) $\frac{3}{4} mgR$

Question 12

An astronaut inside an orbiting space station drops an apple. The space station is in a circular orbit around Earth.

What is the apparent weight of the apple as measured by the astronaut inside the station?

Accepted Answer

A) Zero

Answer

B) Equal to mg

Answer

C) Greater than mg

Answer

D) Equal to half of mg

Question 13

Taking Earth's rotation into account with angular velocity $\omega$ and radius $R$, what is the effective acceleration due to gravity $g'$ at the equator?

Accepted Answer

D) $g - \omega^2 R$

Answer

A) $g$

Answer

B) $g + \omega^2 R$

Answer

C) $g - \frac{1}{2}\omega^2 R$

Question 14

What is the ratio of the escape velocity from Earth's surface to the orbital velocity of a satellite orbiting very close to Earth's surface?

Accepted Answer

B) $\sqrt{2} : 1$

Answer

A) $1 : 1$

Answer

C) $2 : 1$

Answer

D) $1 : \sqrt{2}$

Question 15

A satellite orbiting Earth in a circular orbit of radius $r$ encounters thin atmospheric resistance, causing its orbit radius to decrease to $r/2$.

How does the kinetic energy of the satellite change after moving into this lower circular orbit?

Accepted Answer

C) Doubles

Answer

A) Decreases by half

Answer

B) Remains unchanged

Answer

D) Quadruples

Question 16

What is the gravitational potential at the center of a solid uniform sphere of mass $M$ and radius $R$ (taking potential at infinity as zero)?

Accepted Answer

A) $-\frac{3GM}{2R}$

Answer

B) $-\frac{GM}{R}$

Answer

C) $-\frac{GM}{2R}$

Answer

D) Zero

Question 17

For small distances above and below Earth's surface ($h, d \ll R$), the acceleration due to gravity decreases at both height $h$ and depth $d$.

At what height $h$ above Earth's surface is the decrease in $g$ equal to the decrease in $g$ at a depth of $d = 20 km$ below the surface?

Accepted Answer

B) 10 km

Answer

A) 20 km

Answer

C) 40 km

Answer

D) 5 km

Question 18

Two identical stars, each of mass $M$, move in circular orbits around their common center of mass under their mutual gravitational attraction. The distance between the centers of the two stars is $2R$.

What is the time period $T$ of revolution of each star?

Accepted Answer

C) $4\pi \sqrt{\frac{R^3}{GM}}$

Answer

A) $2\pi \sqrt{\frac{R^3}{GM}}$

Answer

B) $2\pi \sqrt{\frac{2R^3}{GM}}$

Answer

D) $4\pi \sqrt{\frac{2R^3}{GM}}$

Question 19

A body is projected vertically upward from Earth's surface with an initial velocity equal to half of the escape velocity ($v = \frac{1}{2}v_e$).

What is the maximum height $h$ attained by the body above Earth's surface in terms of Earth's radius $R$?

Accepted Answer

B) $R/3$

Answer

A) $R/2$

Answer

C) $R/4$

Answer

D) $2R/3$

Question 20

Statement I: The gravitational force between two point masses is independent of the presence of other bodies and the intervening medium.
Statement II: Gravitational force can be shielded by surrounding a mass with a thick shell of lead.

Which of the following statements is correct regarding the assertions above?

Accepted Answer

C) Statement I is true, but Statement II is false.

Answer

A) Both Statement I and Statement II are true.

Answer

B) Both Statement I and Statement II are false.

Answer

D) Statement I is false, but Statement II is true.

Set 4Grade 11 : Physics - Gravitation