# Physics 9702 Doubts | Help Page 195

__Question 944: [Kinematics > Air resistance]__
A football is dropped from top of a
tall building.

Which acceleration-time graph best
represents motion of the football through the air?

**Reference:**

*Past Exam Paper – June 2008 Paper 1 Q8*

__Solution 944:__**Answer: C.**

Since the motion of the air is
through the air, we should account for the effect of air resistance.

First of all, an acceleration-time
graph is given. So, we need to consider the resultant acceleration of the
football during its motion.

The acceleration of free fall, g
causes a downward acceleration on the ball (due to its weight) and this is a constant
value. Then, as the ball falls, air resistance acts on it due to its motion.
Air resistance opposes motion and thus, acts upwards since ball is falling.
This causes the resultant force, and thus the resultant acceleration of the
ball to

**decrease**with time. [C is correct]
Now, air resistance depends on the
speed of the ball. (Even though acceleration decreases, the speed increases
until the acceleration is zero – remember that acceleration is the rate of
change of velocity, so as long as the acceleration is not zero, the speed will
be changing.) As the speed of the ball increases, the air resistance becomes
greater, until it is equal to the downward weight of the ball.Thus, the decrease in acceleration is not linear.

From this point, the resultant acceleration
of the ball is zero – the ball is said to have reached its terminal speed. Since
speed is no longer changing, air resistance is also constant and equal to
magnitude to the weight.

__Question 945: [Dynamics > Collisions]__
Which statement about a ball that
strikes a tennis racket and rebounds is

**always**correct?
A Total kinetic energy of the ball
is conserved.

B Total kinetic energy of the system
is conserved.

C Total momentum of the ball is
conserved.

D Total momentum of the system is
conserved.

**Reference:**

*Past Exam Paper – November 2009 Paper 11 Q8 & Paper 12 Q7*

__Solution 945:__**Answer: D.**

For an elastic collision, both the
total kinetic energy and total momentum of the system are conserved.

For an inelastic collision, the
total kinetic energy of the system is not conserved but the total momentum of
the system are conserved.

Thus, for any collision, the total
momentum of the system is conserved. Not that the system consists of the ball
and the tennis racket. Even if the velocity of one of them changes, the change
in velocity of the other would account for the conservation of the momentum in
the while system.

__Question 946: [Matter > Changes of States]__
Which row correctly states the
characteristics of the process of evaporation?

**Reference:**

*Past Exam Paper – June 2013 Paper 11 Q20*

__Solution 946:__**Answer: B.**

For a substance to change from the
liquid state to the gaseous state (for both evaporation and boiling), it
requires energy. [C and D are incorrect]

Evaporation can occur at any
temperature, while boiling occurs only at a particular temperature called the
boiling point of the substance. [A is incorrect]

As boiling occurs, the substance
loses some of its molecules that had energy greater than the average energy of
the other molecules of the substance (this is why those molecules could escape
through evaporation). Thus, the average kinetic energy of the molecules of the whole
of the substance is now lower. This is represented as a decrease in
temperature.

__Question 947: [Kinematics > Projectile motion]__
A projectile is launched at point O
and follows path OPQRS, as shown. Air resistance may be neglected.

Which statement is true for the
projectile when it is at the highest point Q of its path?

A The horizontal component of the
projectile’s acceleration is zero.

B The horizontal component of the
projectile’s velocity is zero.

C The kinetic energy of the
projectile is zero.

D The momentum of the projectile is
zero.

**Reference:**

*Past Exam Paper – November 2002 Paper 1 Q8 & June 2005 Paper 1 Q9 & June 2012 Paper 12 Q10*

__Solution 947:__**Answer: A.**

Since the

__acceleration__due to gravity is vertically**downward**, at the highest point Q, where the direction of motion is to the right (horizontal velocity remains constant since air resistance, which opposes motion, is negligible [also, it is not affected by the vertically down acceleration], so the horizontal component of acceleration is zero).
At the highest point Q, there is no
vertical upward component since the projectile has reached its maximum vertical
height – it cannot go any higher.

The horizontal component of the
projectile’s

**velocity is not zero**since the motion continues towards the right (note that zero acceleration does not mean a speed of zero – it just means that the speed is not changing). [B is incorrect]
Both the kinetic energy and momentum
of the projectile depends on its speed. Since the speed is not zero, the
kinetic energy and momentum cannot be zero. [C and
D are incorrect]

__Question 948: [Gravitation]__
The radius of the orbit of a plant X
round the sun is 4 times the orbital radius of Earth. If a year on the planet
is assumed to be the period of its revolution round the sun, what is the
equivalent age of an eighty year old man in terms of the year on the planet X?

A 10 B 20 C 80 D 320 E 640

**Reference:**

*Pacific Physics A-Level, Volume 1 by POH LIONG YONG – Self Evaluation Exercise 9.2 Q7*

__Solution 948:__**Answer: A.**

To answer this question, we need to
use

**Kepler’s 3**which gives the relationship between the period and the radius of orbit of a planet. The law is derived below.^{rd}law of Gravitation
Suppose that a planet of mass m is
in a circular orbit of radius r around the sun.

The centripetal force F is provided
by the gravitational attraction on the planet by the sun.

F = GMm / r

^{2}where M is the mass of sun
Therefore, GMm / r

^{2}= mrÏ‰^{2}
GMm / r

^{2}= mr (2Ï€ / T)^{2}where T = period
T

^{2}/ r^{3}= 4Ï€^{2}/ GM = constant (4Ï€^{2}/ GM has a constant value)
T

^{2}/ r^{3}= constant**T**

^{2}**∝**

**r**

^{3}
This relationship is known as

**Kepler’s 3**.^{rd}law of Gravitation
Let the radius of the orbit of earth
round the sun be R

_{E}.
Radius of planet X round the sun = 4R

_{E}
Let the period of revolution of
earth round the sun to be T

_{E}and that of planet X to be T_{X}.
From Kepler’s 3

^{rd}law of gravitation,
T

^{2}∝ r^{3}
T

^{2}/ r^{3}= constant
For Earth, T

_{E}^{2}/ R_{E}^{3}= constant
For planet X, T

_{X}^{2}/ (4R_{E})^{3}= constant
Since both are orbiting round the
sun, the ‘constant’ is the same in both cases.

T

_{X}^{2}/ (4R_{E})^{3}= T_{E}^{2}/ R_{E}^{3}
T

_{X}^{2}= 64R_{E}^{3}× (T_{E}^{2}/ R_{E}^{3}) = 64T_{E}^{2}
Period of revolution of planet X, T

_{X}= 8T_{E}
That is, 1 year on planet X is
equivalent to 8 years on earth. Thus, an 80-year old man on earth would have an
equivalent age of 80 / 8 = 10 years on planet X.

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