# Physics 9702 Doubts | Help Page 158

__Question 782: [Current of Electricity]__
In circuit shown, the resistance of
the thermistor decreases as temperature increases.

Which graph shows variation with
Celsius temperature θ of potential difference V between points P and Q?

**Reference:**

*Past Exam Paper – November 2013 Paper 13 Q37*

__Solution 782:__**Answer: C.**

V is the p.d.
across the fixed resistor.

From Kirchhoff’s
law, the sum of p.d. across the thermistor and the p.d. across the fixed
resistor is equal to the e.m.f. of the d.c. supply.

Ohm’s law: V =
IR

As the temperature
increases, the resistance of the thermistor decreases, and hence the p.d.
across it also decreases since V = IR. Thus, as temperature increases, the p.d.
V across the fixed resistor increases (so that the sum of p.d.’s is always
equal to the e.m.f.). [A and B are incorrect]

But the
resistance of a thermistor does not vary linearly with temperature. So, the
increase in the p.d. V with the temperature is not linear.

__Question 783: [Measurement > Uncertainty]__
Diagram shows an experiment to
measure speed of a small ball falling at constant speed through a clear liquid
in a glass tube.

There are two marks on the tube. Top
mark is positioned at 115 ± 1 mm on the adjacent rule and the lower mark at 385
± 1 mm. The ball passes the top mark at 1.50 ± 0.02 s and passes the lower mark
at 3.50 ± 0.02 s.

Constant speed of the ball is
calculated by (385 – 115) / (3.50 – 1.50) = 270 / 2.00 = 135 mms

^{-1}.
Which expression calculates
fractional uncertainty in the value of this speed?

**Reference:**

*Past Exam Paper – June 2011 Paper 11 Q5 & Paper 13 Q4*

__Solution 783:__**Answer: A.**

Speed v = Distance s / Time t

Δv / v = (Δs / s) + (Δt / t)

Fractional uncertainty of speed = Δv / v

Distance s = 385 – 115 = 270 mm

Δs = ± (1 + 1) = ± 2 mm

Time t = 3.50 – 1.50 = 2.00s

Δt = ± (0.02 + 0.02) = ± 0.04 s

__Question 784: [Kinematics]__
Diagram shows a laboratory
experiment in which a feather falls from rest in a long evacuated vertical tube
of length L.

The feather takes time T to fall from
top to the bottom of the tube.

How far will the feather have fallen
from the top of the tube in time 0.50 T?

A 0.13 L B 0.25 L C
0.38 L D 0.50 L

**Reference:**

*Past Exam Paper – June 2012 Paper 11 Q8 & Paper 13 Q9*

__Solution 784:__**Answer: B.**

Since a vacuum, there is no air
resistance.

Initial speed, u = 0 since the
feather falls from

**rest**.
The acceleration of free fall, g,
acts downwards.

Equation for uniformly accelerated
motion: s = ut + ½ at

^{2}
When distance s = L, the time taken
to fall = T

L = 0 + 0.5gT

^{2}= 0.5gT^{2}
When time to fall = 0.5T, let the
distance be s

s = 0 + 0.5g(0.5T)

^{2}
Distance s = gT

^{2}/ 8
From L = 0.5gT

^{2}, gT^{2}= 2L
Distance s = gT

^{2}/ 8 = 2L / 8 = L/4 = 0.25L

__Question 785: [Dynamics > Resultant force]__
Diagrams show a metal cube suspended
from a spring balance before and during immersion in water.

A reduction in the balance reading
occurs as a consequence of the immersion.

Which statement is correct?

A The balance reading will be
further reduced if the cube is lowered further into the water.

B The balance reading during
immersion corresponds to the upthrust of the water on the cube.

C The forces acting on the vertical
sides of the cube contribute to the change in the balance reading.

D The gravitational pull on the cube
is unchanged by the immersion.

**Reference:**

*Past Exam Paper – November 2010 Paper 12 Q13*

__Solution 785:__**Answer: D.**

Before the immersion, the balance
reads the weight of the object, which is downwards. The weight of the cube is
the gravitational pull on the cube and this is unchanged in a specific location
since weight W = mg. [D is correct]

As the cube in immersed, it
experiences an upthrust force upwards. This force is due to the difference in
pressures acting on the top and bottom of the cube.

Pressure = hρg

Since the cube has a specific size,
the difference pressure acting on the cube, as long as it is fully immersed, is
unchanged. Thus, the upthrust is unchanged no matter how further the cube is
immersed. [A is incorrect]

The forces acting on the vertical
sides of the cube contribute are equal in magnitude since they acts at the same
depth in the water. So, they cancel each other and are not the cause in the
change in the balance reading. [C is incorrect]

Thus, the balance reading is not the
upthrust but the weight (which acts downwards) minus the upthrust (which acts
upwards). The balance reads the resultant. [B is
incorrect]

__Question 786: [Work, Energy and Power]__
Steel ball is falling at constant
speed in oil.

Which graph shows variation with
time of the gravitational potential energy E

_{p}and the kinetic energy E_{k}of the ball?**Reference:**

*Past Exam Paper – June 2005 Paper 1 Q15 & June 2008 Paper 1 Q18*

__Solution 786:__**Answer: B.**

Kinetic energy E

_{k}= ½ mv^{2}
Since the speed is constant, the
kinetic energy is also constant.

Gravitational potential energy E

_{p}= mgh
Speed = Distance / Time

As the speed is constant, the rate
at which the distance (h) decreases is constant. So

_{}, the decrease in E_{p}is also constant.