• Physics 9702 Doubts | Help Page 178

Question 879: [Measurement]

Uncertainty in the value of the momentum of a trolley passing between two points X and Y varies with the choice of measuring devices.

Measurements for the same trolley made by different instruments were recorded.

1 distance between X and Y using a metre rule with cm divisions = 0.55 m

2 distance between X and Y using a metre rule with mm divisions = 0.547 m

3 timings using a wristwatch measuring to the nearest 0.5 s at X = 0.0 s and at Y = 4.5 s

4 timings using light gates measuring to the nearest 0.1 s at X = 0.0 s and at Y = 4.3 s

5 mass of trolley using a balance measuring to the nearest g = 6.4 × 10^–2 kg

6 mass of trolley using a balance measuring to the nearest 10 g = 6 × 10^–2 kg

Which measurements, one for each quantity measured, lead to the least uncertainty in the value of the momentum of the trolley?

A 1, 3 and 6                B 1, 4 and 6                C 2, 3 and 6                D 2, 4 and 5

Reference: Past Exam Paper – June 2011 Paper 12 Q4

Solution 879:

Answer: D.

We need to identify which of the measurements would give the least uncertainty in the value of the momentum of the trolley.

Momentum p = mv = ms / t

where s is the distance between X and Y

Δp / p = (Δm / m) + (Δs / s) + (Δt / t)

For the uncertainty in the momentum, Δp, to have to least value, the uncertainties in the quantities measured should be smallest. That is Δm, Δs and Δt should be small. This is observed to be the case for measurements 2, 4 and 5, compared to the corresponding quantity measured.

Question 880: [Simple harmonic motion]

(a)

(i) Define simple harmonic motion.

(ii) On the axes of Fig.1, sketch variation with displacement x of the acceleration a of a particle undergoing simple harmonic motion.

(b) A strip of metal is clamped to the edge of a bench and a mass is hung from its free end as shown in Fig.2.

The end of the strip is pulled downwards and then released. Fig.3 shows variation with time t of the displacement y of the end of the strip.

On Fig.4, show corresponding variation with time t of the potential energy E_p of the vibrating system.

(c) The string supporting the mass breaks when the end of the strip is at its lowest point in an oscillation. Suggest what change, if any, will occur in period and amplitude of the subsequent motion of the end of the strip.

Reference: Past Exam Paper – June 2002 Paper 4 Q4

Solution 880:

(a)

(i) In simple harmonic motion, the acceleration is proportional to the displacement / distance (from fixed points) and it is directed towards a fixed point.

(ii) The graph is a straight line through the origin, in the quadrants 2 and 4.

(b) The graph is a sinusoidal curve, all about the t-axis. It should have the correct period and a correct ‘phase’.

(c) The period is shorter. The amplitude is larger.

Question 881: [Matter > Deformation of Solids]

Two steel wires P and Q have lengths l and 2l respectively, and cross-sectional areas A and A / 2 respectively. Both wires obey Hooke’s law.

What is the ratio (tension in P / tension in Q) when both wires are stretched to the same extension?

A 1 / 4                         B 1 / 2                         C 2 / 1                         D 4 / 1

Reference: Past Exam Paper – June 2005 Paper 1 Q22 & June 2009 Paper 1 Q20

Solution 881:

Answer: D.

Since both wires are made of steel, they have the same Young modulus E.

Young modulus E = stress / strain

Stress = Tension / Area = F / A

Strain = extension / original length = e / L

Young modulus E = (F/A) / (e/L) = FL / Ae

Tension F = EAe / L

For wire P: F_P = EAe / l

For wire Q: F_Q = E (A/2) e / (2l) = EAe / 4l = F_P / 4

Ratio = F_P / F_Q = F_P / (F_P/4) = 4 / 1

 

• 9702 June 2007 Paper 2 Worked Solutions | A-Level Physics

Question 1
{Detailed explanations for this question is available as Solution 556 at Physics 9702 Doubts | Help Page 109 - http://physics-ref.blogspot.com/2015/04/physics-9702-doubts-help-page-109.html}




Question 2
{Detailed explanations for this question is available as Solution 871 at Physics 9702 Doubts | Help Page 175 - http://physics-ref.blogspot.com/2015/06/physics-9702-doubts-help-page-175.html}




Question 3
{Detailed explanations for this question is available as Solution 238 at Physics 9702 Doubts | Help Page 38 - http://physics-ref.blogspot.com/2014/12/physics-9702-doubts-help-page-38.html}




Question 4
{Detailed explanations for this question is available as Solution 262 at Physics 9702 Doubts | Help Page 43 - http://physics-ref.blogspot.com/2015/01/physics-9702-doubts-help-page-43.html}




Question 5
{Detailed explanations for this question is available as Solution 1006 at Physics 9702 Doubts | Help Page 209 - http://physics-ref.blogspot.com/2015/10/physics-9702-doubts-help-page-209.html}




Question 6
{Detailed explanations for this question is available as Solution 874 at Physics 9702 Doubts | Help Page 176 - http://physics-ref.blogspot.com/2015/06/physics-9702-doubts-help-page-176.html}



Question 7
The radioactive decay of a strontium (Sr) nucleus is represented in Fig. 7.1.


Explanations have been provided for questions that were found to be more difficult. If you are having other doubts that have not been explained here, you may ask your questions through comments.

• 9702 November 2014 Paper 43 Worked Solutions | A-Level Physics

Paper 43

Question 2
{Detailed explanations for this question is available as Solution 624 at Physics 9702 Doubts | Help Page 123 - http://physics-ref.blogspot.com/2015/04/physics-9702-doubts-help-page-123.html}







Question 4
{Detailed explanations for this question is available as Solution 632 at Physics 9702 Doubts | Help Page 125 - http://physics-ref.blogspot.com/2015/04/physics-9702-doubts-help-page-125.html}



Question 5

(a) Define electric potential at a point.

(b) An isolated metal sphere is charged to a potential V. The charge on the sphere is q.

The charge on thesphere may be considered to act as a point charge at the centre of the sphere.

Question 6
{Detailed explanations for this question is available as Solution 1001 at Physics 9702 Doubts | Help Page 208 - http://physics-ref.blogspot.com/2015/10/physics-9702-doubts-help-page-208.html}





Question 8
{Detailed explanations for this question is available as Solution 563 at Physics 9702 Doubts | Help Page 110 - http://physics-ref.blogspot.com/2015/04/physics-9702-doubts-help-page-110.html}





Question 9
{Detailed explanations for this question is available as Solution 653 at Physics 9702 Doubts | Help Page 130 - http://physics-ref.blogspot.com/2015/05/physics-9702-doubts-help-page-130.html}





Question 10
{Detailed explanations for this question is available as Solution 1036 at Physics 9702 Doubts | Help Page 217 - http://physics-ref.blogspot.com/2015/10/physics-9702-doubts-help-page-217.html}






Question 11
{Detailed explanations for this question is available as Solution 615 at Physics 9702 Doubts | Help Page 121 - http://physics-ref.blogspot.com/2015/04/physics-9702-doubts-help-page-121.html}





Question 12
{Detailed explanations for this question is available as Solution 1075 at Physics 9702 Doubts | Help Page 227 - http://physics-ref.blogspot.com/2015/12/physics-9702-doubts-help-page-227.html}




Explanations have been provided for questions that were found to be more difficult. If you are having other doubts that have not been explained here, you may ask your questions through comments.

• Physics 9702 Doubts | Help Page 177

Question 877: [Circular motion]

A large bowl is made from part of a hollow sphere.

A small spherical ball is placed inside the bowl and is given a horizontal speed. The ball follows a horizontal circular path of constant radius, as shown in Fig.1.

The forces acting on the ball are its weight W and the normal reaction force R of the bowl on the ball, as shown in Fig.2.

The normal reaction force R is at an angle θ to the horizontal.

(a)

(i) By resolving reaction force R into two perpendicular components, show that the resultant force F acting on the ball is given by the expression

W = F tan θ.

(ii) State significance of the force F for the motion of the ball in the bowl.

(b) The ball moves in circular path of radius 14 cm. For this radius, the angle θ is 28°. Calculate the speed of the ball.

Reference: Past Exam Paper – November 2014 Paper 41 & 42 Q2

Solution 877:

(a)

(i)

{The weight acts vertically down, so it does not have any horizontal component. The force component of the force F is then only due to the horizontal component of the reaction force R.}

F = R cosθ

{The path is circular with a constant radius. This means that the ball does not move up or down in the surface of the sphere. Thus, the resultant vertical component of the force on the ball is zero – that is, the vertical upward component of the reaction force R is equal to the downward weight.}

W = R sinθ

{Dividing the equations eliminate R and gives the required expression.}

dividing, W = F tanθ

(ii) The force F provides the centripetal force.

(b)

{As shown above, W = F tanθ. The weight W is equal to mg. The resultant force F provides the centripetal force, given by mv² / r. Replacing these in the equation (W = F tanθ) allows us to solve for speed v.}

EITHER F = mv² / r and W = mg

{W = F tanθ giving mg = (mv² / r) tan θ}

OR v² = rg / tan θ

v² = (14×10^–2 × 9.8) / tan 28° = 2.58

Speed v = 1.6 m s^–1

Question 878:

A thermometer can be read to accuracy of ± 0.5 °C. This thermometer is used to measure a temperature rise from 40 °C to 100 °C.

What is percentage uncertainty in the measurement of the temperature rise?

A 0.5 %                       B 0.8 %                       C 1.3 %                       D 1.7 %

Reference: Past Exam Paper – November 2003 Paper 1 Q4 & June 2014 Paper 12 Q5

Solution 878:

A thermometer can be read to an accuracy of ± 0.5 °C. This thermometer is used to measure a temperature rise from 40 °C to 100 °C.

• 9702 November 2014 Paper 22 Worked Solutions | A-Level Physics

Paper 22

Question 1
{Detailed explanations for this question is available as Solution 688 at Physics 9702 Doubts | Help Page 139 - http://physics-ref.blogspot.com/2015/05/physics-9702-doubts-help-page-139.html}





Question 2
{Detailed explanations for this question is available as Solution 527 at Physics 9702 Doubts | Help Page 102 - http://physics-ref.blogspot.com/2015/04/physics-9702-doubts-help-page-102.html}





Question 3
{Detailed explanations for this question is available as Solution 1030 at Physics 9702 Doubts | Help Page 215 - http://physics-ref.blogspot.com/2015/10/physics-9702-doubts-help-page-215.html}





Question 5
{Detailed explanations for this question is available as Solution 1123 at Physics 9702 Doubts | Help Page 242 - http://physics-ref.blogspot.com/2016/09/physics-9702-doubts-help-page-242.html}





Question 6
{Detailed explanations for this question is available as Solution 1082 at Physics 9702 Doubts | Help Page 229 - http://physics-ref.blogspot.com/2015/12/physics-9702-doubts-help-page-229.html}





Question 7
In the decay of a nucleus of 21084 Po, an α-particle is emitted with energy 5.3 MeV.



Explanations have been provided for questions that were found to be more difficult. If you are having other doubts that have not been explained here, you may ask your questions through comments.