Practice Questions
Questions 1–3 refer to a ball of mass m on
a string of length R, swinging around in circular
motion, with instantaneous velocity v and centripetal
acceleration a.
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| 1. |
What is
the centripetal acceleration of the ball if the length of the string
is doubled? |
| (A) |
a/4 |
| (B) |
a/2 |
| (C) |
a |
| (D) |
2a |
| (E) |
4a |
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| 2. |
What is
the centripetal acceleration of the ball if the instantaneous velocity
of the ball is doubled? |
| (A) |
a/4 |
| (B) |
a/2 |
| (C) |
a |
| (D) |
2a |
| (E) |
4a |
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| 3. |
What is
the centripetal acceleration of the ball if its mass is doubled? |
| (A) |
a/4 |
| (B) |
a/2 |
| (C) |
a |
| (D) |
2a |
| (E) |
4a |
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| 4. |
A bullet of mass m traveling
at velocity v strikes a block of mass 2m that
is attached to a rod of length R. The bullet collides
with the block at a right angle and gets stuck in the block. The
rod is free to rotate. What is the centripetal acceleration of the
block after the collision? |
| (A) |
v2/R |
| (B) |
(1/2)v2/R |
| (C) |
(1/3)v2/R |
| (D) |
(1/4)v2/R |
| (E) |
(1/9)v2/R |
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| 5. |
A car wheel drives over a pebble,
which then sticks to the wheel momentarily as the wheel displaces it.
What is the direction of the initial acceleration of the pebble? |
| (A) |
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| (B) |
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| (C) |
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| (D) |
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| (E) |
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| 6. |
If
we consider the gravitational force F between two
objects of masses  and  respectively, separated by a distance R,
and we double the distance between them, what is the new magnitude
of the gravitational force between them? |
| (A) |
F/4 |
| (B) |
F/2 |
| (C) |
F |
| (D) |
2F |
| (E) |
4F |
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| 7. |
If
the Earth were compressed in such a way that its mass remained the
same, but the distance around the equator were just one-half what
it is now, what would be the acceleration due to gravity at the surface
of the Earth? |
| (A) |
g/4 |
| (B) |
g/2 |
| (C) |
g |
| (D) |
2g |
| (E) |
4g |
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| 8. |
A
satellite orbits the Earth at a radius r and a
velocity v. If the radius of its orbit is doubled,
what is its velocity? |
| (A) |
v/2 |
| (B) |
v/ |
| (C) |
v |
| (D) |
 v |
| (E) |
2v |
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| 9. |
An
object is released from rest at a distance of  from the center of the Earth, where  is the radius of the Earth. In terms of
the gravitational constant (G), the
mass of the Earth (M), and  , what is the velocity of the object when
it hits the Earth? |
| (A) |
 |
| (B) |
 |
| (C) |
 |
| (D) |
 |
| (E) |
 |
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| 10. |
Two
planets, A and B, orbit a star.
Planet A moves in an elliptical orbit whose semimajor
axis has length a. Planet B moves
in an elliptical orbit whose semimajor axis has a length of 9a.
If planet A orbits with a period T,
what is the period of planet B’s orbit? |
| (A) |
729T |
| (B) |
27T |
| (C) |
3T |
| (D) |
T/3 |
| (E) |
T/27 |
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