# Physics 9702 Doubts | Help Page 22

__Question 116: [Moment > Equilibrium > Graph]__Horizontal bar is supported on pivot at its centre of gravity. Fixed load is attached to one end of the bar. To keep bar in equilibrium, a force F is applied at distance x from the pivot.

How does F vary with x?

**Reference:**

*Past Exam Paper – June 2013 Paper 11 Q14*

__Solution 116:__**Answer: B.**

The fixed load causes an
anticlockwise moment on the bar.

**Moment = Force x Perpendicular distance of force from pivot**

Since the load is fixed (its distance from the pivot does not change), the
magnitude of the anticlockwise moment is also constant (Let
this magnitude be M

_{A}).
For

**equilibrium**, the force F, acting at a distance x, causes a clockwise moment with a magnitude equal to the anticlockwise moment (M_{A}).
So, for equilibrium, Fx = M

_{A}giving F = M_{A}/ x.
Therefore, by increasing distance s,
a smaller value of force F is required. [C and D
are incorrect]

Now, consider the following:

If distance x is doubled, only
half the value of force F is needed and if this distance x is doubled, there
cannot possibly be a distance where zero force is force. A force will always be needed to cause the moment, no matter how
long the distance x is. Thus, the graph cannot be a straight line [A is incorrect] but should rather be a graph
where force F never goes to zero.

__Question 117: [Current of Electricity > Potential difference]__Constant 60 V d.c. supply is connected across two resistors of resistance 400 kΩ and 200 kΩ.

What is the reading on voltmeter, also of resistance 200 kΩ, when connected across 200 kΩ resistor as shown in diagram?

A 12 V B 15 V C 20 V D 30 V

**Reference:**

*Past Exam Paper – November 2011 Paper 12 Q38*

__Solution 117:__**Answer: A.**

Equivalent resistance of voltmeter
and resistor in parallel = [1/200 + 1/200]

^{-1}= 100
From Kirchhoff’s law, for
components in series, the sum of potential differences across the components is
equal to the e.m.f. in the circuit. Thus,
the sum of the p.d. across the 400 kΩ and the p.d. across the equivalent
resistance of 100 kΩ must be equal to the e.m.f of 60V in the circuit.

Additionally, there is the same p.d.
across components in parallel.

From the

**, the p.d. across the components in parallel is**__potential divider equation__
p.d. = [100 / (100+400)] x 60 = 12V

__Question 118: [Waves > Interference > Double Slits]__Coherent monochromatic light illuminates two narrow parallel slits and interference pattern that results is observed on screen some distance beyond the slits.

Which change increases separation between the dark lines of interference pattern?

A using monochromatic light of higher frequency

B using monochromatic light of longer wavelength

C decreasing the distance between screen and the slits

D increasing distance between the slits

**Reference:**

*Past Exam Paper – November 2002 P1 Q28*

__Solution 118:__**Answer: B.**

__For a double slit__:

**x = λD / a**

where

x is the separation between fringes

λ is the wavelength of the light

D is the distance between the screen and the slits

a is the distance between the slits

A light of higher frequency would have a

__smaller wavelength__(λ = c / f). This would cause the separation between the dark fringes of the interference pattern to decrease.

Using monochromatic light of a longer wavelength increases the separation of fringes.

Decreasing the distance between the screen and the slits or increasing the distance between the slits would each cause the separation of the fringes to decrease

__Question 119: [Dynamics > Momentum]__Object of mass 4.0 kg moving with speed of 3.0 m s

^{–1}strikes a stationary object in an inelastic collision.

Which statement is correct?

A After collision, total kinetic energy is 18 J.

B After collision, total kinetic energy is less than 18 J.

C Before collision, total kinetic energy is 12 J.

D Before collision, total kinetic energy is less than 12 J.

**Reference:**

*Past Exam Paper – June 2014 Paper 11 Q9*

__Solution 119:__**Answer: B.**

In an inelastic collision,
kinetic energy is not conserved.

Before collision,

Kinetic energy, KE = ½ mv

^{2}+ 0 = ½ (4.0)(3)^{2}= 18J [C and D are incorrect]
Since collision is inelastic,
kinetic energy is less than 18J after collision.

__Question 120: [Current of Electricity > Potentiometer]__In circuit below, P is potentiometer of total resistance 10 Ω and Q is fixed resistor of resistance 10 Ω.

Battery has an e.m.f. of 4.0 V and negligible internal resistance. Voltmeter has very high resistance.

Slider on potentiometer is moved from X to Y and graph of voltmeter reading V is plotted against slider position.

Which graph would be obtained?

**Reference:**

*Past Exam Paper – November 2010 Paper 11 Q37 & Paper 13 Q35 & November 2013 Paper 11 & 12 Q36*

__Solution 120:__**Answer: A.**

When the slider is at X {at X, resistance of the potentiometer is taken to be zero},
the voltmeter must read 4 V.

{The flow of current is as
follows: from the positive terminal – through the moving jack until the point
it is connected on resistor P – from P to end X – through the voltmeter and
back to the negative terminal of the supply (no current goes through Q).}

When the slider is moved to Y, the potentiometer
P and the voltmeter are in series {no current flows
through Q – resistor Q can be said to be short circuited in both cases} with
almost all the resistance in the voltmeter {as stated
in the question, the voltmeter has a very high resistance – Ohm’s law: V = IR –
since the total resistance of the potentiometer is negligible compared to that
of the voltmeter}, and hence the p.d. across the voltmeter is still 4 V.

{This can be verified
using the potential divider equation:

**V**. Let R_{1}= [R_{1}/ (R_{1}+R_{2})] V_{1}be the resistance of the voltmeter. Since the voltmeter has a very high resistance, R_{1}>> R_{2}, where R_{2}is the resistance of the potentiometer. Hence, (R_{1}+ R_{2}) ≈ R_{1}and V_{1}= V}Therefore, the voltmeter reading remains 4V as the slider is moves from X to Y.

In a proper circuit, a voltmeter is usually connected in parallel to a component if we want to know the p.d. across that component. Connecting a voltmeter in series results in the above situation where the voltmeter always reads 4V.

__Question 121: [Current of Electricity > Potentiometer]__12 V battery is in series with ammeter, 2 Ω fixed resistor and a 0 – 10 Ω variable resistor. High-resistance voltmeters P and Q are connected across variable resistor and fixed resistor respectively, as shown.

Resistance of variable resistor is changed from its maximum value to zero.

Which graph shows variation with current of voltmeter readings?

**Reference:**

*Past Exam Paper – June 2013 Paper 12 Q36*

__Solution 121:__**Answer: D.**

Since the variable resistor and the
fixed resistor are in series, the total e.m.f. in the circuit is divided
between them. The high-resistance voltmeters P and Q are connected across (in
parallel) them.

Components with high
resistance tend to prevent current from flowing. So, at a junction for
components in parallel, most current will tend to flow in the component with
smaller resistance (considering P and the variable resistor, most current would
flow in the variable resistor).

Additionally, from Kirchhoff’s law,
the potential difference across P and the variable is the same. This is also
true for the potential difference across the 2Ω resistor and Q.

The potential difference across each
of these resistors may be obtained from the

**:**__potential divider equation__**V**._{1}= [R_{1}/ (R_{1}+R_{2})] V
Let R

_{1}be the resistance of the variable resistor and R_{2}be the resistance of the fixed resistor. As R_{1}is decreased, the p.d. across it decreases. When R_{1}= 0, V_{1}= 0. Thus, the voltmeter reading of P should give zero. [Graph D is correct since it shows that P is decreasing and going to zero]
Decreasing R

_{1}causes the p.d. across the fixed resistor to increases. This same p.d. is across Q.
what does this mean ≈

ReplyDeleteapproximately equal to

DeleteYou are amazing. You have solved so many of my doubts. Thank you so very much. Really.

ReplyDeletenov 2012 13 q 24 pls

ReplyDeletesee solution 960 at

Deletehttp://physics-ref.blogspot.com/2015/09/physics-9702-doubts-help-page-198.html

Hey Thank you so much for the explanation. I have doubt on Q120. Why would the current choose the path through the voltmeter with very high resistance instead of resistors P & Q? At first glance I thought there isn't any reading on the voltmeter

ReplyDeleteP is a potentiometer and this work in a different way than does a fixed resistor. In this case, current would always flow form the jack to end X. Then, for the current to flow in a complete circuit, the only possible path is through the voltmeter.

DeleteFor any position of the jack, the voltmeter reading would remain the same due to its very high resistance compared to that of the potentiometer.

For Q120, why would the current choose to go through the voltmeter when it has very high resistance?

ReplyDeleteit's very high but not infinite, so a small amount of current would go through it

DeleteFor Q120, when the slider is at X, the voltmeter is connected parallel to P and Q, so it is measuring potential difference across both. A quick calculation tells us that this is 4V. (Each gets 2V because both have the same resistance of 10 ohms when the potentiometer jack is at X.)

ReplyDeleteWhen the slider is at Y, the potentiometer is in series with the voltmeter. So, the voltmeter is really just connected parallel to Q. No (or very little) current flows through the P and voltmeter due to the the high resistance of the voltmeter. Hence, the voltmeter is measuring the p.d. across Q only, which is 4V.

Hope this helped.