# Physics 9702 Doubts | Help Page 42

__Question 255: [Physical Quantities & Units > Units]__An alternative form of the unit of resistance, the ohm (Ω), is VA

^{-1}.

Which of the following examples shows a similar correct alternative form of unit?

Unit Alternative
form

A coulomb (C) As^{-1}

B farad (F) VC

^{-1}

C pascal (Pa) Nm

^{-2}

D volt (V) JC

E watt (W) Js

**Reference:**

*Past Exam Paper – J91 / I / 1*

__Solution 255:__**Answer: C.**

Coulomb is the unit of charge. Charge = Current (I) x Time (t). Units of charge = As

Farad is the unit of capacitance. Capacitance = Charge (Q) / Voltage (V). Units of capacitance = CV

^{-1}

Pascal is the unit of pressure. Pressure = Force (F) / Area (A). Units of pressure = Nm

^{-2}

__Question 256: [Dynamics > Laws of motion]__When an object moves up in the sky, the resultant force acting on the object is upwards right?

__Solution 256:__This depends on how the object is moving. Consider the following cases [for all the cases, the velocity being considered is that after the different forces acting on the object have already been considered (e.g. force due to engine, air resistance, gravity, … )]:

__Case 1__:

The object is moving always upwards at

__constant__velocity. The acceleration is thus zero. Since Force F = ma, the resultant force on the object is zero.

__Case 2__:

As the object moves upwards, its velocity is increasing. Therefore, there is an upward acceleration. The resultant force is upwards.

__Case 3__:

As the object moves upwards, its velocity is decreasing. Therefore, there is a downward acceleration, causing the resultant force to be downward.

__Question 257: [Energy > Conservation of energy]__When bungee jumping, student starts with maximum gravitational potential energy (position 1), then falls freely until the rope fully unwinds (position 2), after which the rope starts to stretch until the lowest point of the jump is reached (position 3).

What are kinetic and elastic potential energies at position 3?

**Reference:**

*Past Exam Paper – November 2007 Paper 1 Q16*

__Solution 257:__**Answer: C.**

From the conservation of energy, the sum of energies at position 2 or 3 should be equal to the initial amount of gravitational potential energy the student has at position 1.

Stretching of the rope causes it to have elastic potential energy. Kinetic energy is associated with motion (speed).

At position 2, the rope fully unwinds but it does not stretch. So, it does not have elastic potential energy. The kinetic energy is maximum at position 2.

At position 3, the rope is stretched. So, it has elastic potential energy. Also, at position 3, the lowest point of the jump is reached. So, the student will not move further below (no further motion below). Thus, the kinetic energy is minimum. (As stated before, the total energy should be equal to the initial gravitational potential energy, so the kinetic energy cannot be maximum too. Energy would not be conserved.)

__Question 258: [Measurements > Graphs]__Calibration graph is produced for faulty ammeter.

Which ammeter reading will be nearest to correct value?

A 0.2 A B 0.4 A C 0.6 A D 0.8 A

**Reference:**

*Past Exam Paper – November 2008 Paper 1 Q5*

__Solution 258:__**Answer: D.**

The calibration graph is a graph of ‘ammeter
reading / A’ on the y-axis against ‘true current / A’ on the x-axis.

For the ammeter reading to
be nearest to the correct value, the y-coordinate of a point (its ammeter
reading) should be closest to the x-coordinate of the same point (the true
current).

Of the 4 choices, only the point at
0.8A has the x- and y-coordinates to be almost the same.

__Question 259: [Measurements]__A metre rule is used to measure length of a piece of wire. It is found to be 70 cm long to nearest millimetre.

How should this result be recorded in table of results?

A 0.7 m B 0.70 m C 0.700 m D 0.7000 m

**Reference:**

*Past Exam Paper – November 2010 Paper 12 Q4*

__Solution 259:__**Answer: C.**

1 mm = 0.1 cm = 0.001m

Measurement = 70.0cm = 0.700m

(Since the metre rule can read to
the nearest millimeter, here 3 significant figures are necessary)

__Question 260: [Kinematics > Linear motion]__A ball was dropped from the window of an apartment located at the tenth storey of a high rise building. 1 second after release, the ball was observed to have fallen by exactly 2 storeys. At which storey will the ball be 2 seconds after it was released?

**Reference:**

*???*

__Solution 260:__Let the distance between 2 consecutive storeys be x. (Assume this is constant for every storey)

There is an acceleration due to gravity downwards. Let acceleration due to gravity, a = 9.81ms

^{-2}. Assume that there gravity is the only force acting on the ball (resistive forces are negligible).

Distance travelled from window, s = ut + ½ at

^{2}

Initial velocity, u = 0.

When time t = 1s, distance s = 2x.

2x = 0 + 0.5 (9.81) (1)

^{2}= 4.905m

Distance x (= 4.905 / 2 = 2.4525m) corresponds to the distance between 2 consecutive storeys.

When time t = 2s,

Distance s = 0 + 0.5 (9.81) (2)

^{2}= 19.62m

Number of storeys = 19.62 / 2.4525 = 8

__Question 261: [Waves > Damping > Graphs]__Refer to November 2007 paper 4 Q3(b)(ii)2 at http://physics-ref.blogspot.com/2014/09/9702-november-2007-paper-4-worked.html

**Reference:**

*Past Exam Paper – November 2007 Paper 4 Q3 (b) (ii) 2*

__Solution 261:__
EITHER

The total energy is now 1.0mJ, but
regardless of the total energy, the graph would have the same basic shape. The
amplitude is read at the value of x (for the new graph) where the kinetic
energy is zero – that is energy is potential.

[I recommend you draw
a rough diagram on the graph as you are reading the explanation below to better
understand.]

So, just imagine a graph of the same
shape, with the total energy = 1.00mJ (that is, at x = 0, kinetic energy is
1.0mJ). This curve would have a lower value of x when the kinetic energy is
zero.

Now, imagine the point where the
kinetic energy is zero on the new curve. Draw a dotted vertical line from that
point until it reaches another point on the curve ALREADY given. At what value
of kinetic energy would this correspond on the previous curve? It would
correspond to a value of (2.56 – 1.00)mJ on the previous curve because the new
curve has the same shape but has its peak value of kinetic energy at 1.00mJ.

So, read the value of x at (2.56 –
1.00)mJ on the previous curve. This would give the amplitude for a total energy
of 1.00mJ. The value of x is about 0.5cm.

OR

Maximum kinetic energy = ½ mω

^{2}a^{2}
At maximum amplitude a, the energy
is entirely potential.

From the formula, it can
be seen that the energy is directly proportional to (amplitude, a)

^{2}. Refer to the case given (before damping) as case 1 and refer to the case with reduced energy as case 2.
For case 1: amplitude, a

_{1}^{2}is proportional to energy E_{1}. Amplitude a_{1}= 0.8cm and energy E_{1}= 2.56mJ.
For case 2: amplitude, a

_{2}^{2}is proportional to energy E_{2}. Amplitude a_{2}= ??? and energy E_{2}= 1.00mJ.
Now, consider the ratio of case 2 to
case 1,

(a

_{2}/ a_{1})^{2}= E_{2}/ E_{1}
Amplitude a

_{2}= [√( E_{2}/ E_{1})] x a_{1}= [√(1.00 / 2.56)] x 0.8 = 0.5cm
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