# 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)

__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.

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

_{P}= mgh where h is the magnitude of the displacement y. Energy is a scalar and cannot have a negative value. At the equilibrium position (y = 0), h = 0 and so, E

_{p}= 0.}

**(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 2*l*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 / (2*l*) = EAe / 4*l*= F_{P}/ 4
Ratio = F

_{P}/ F_{Q}= F_{P}/ (F_{P}/4) = 4 / 1
This comment has been removed by the author.

ReplyDeleteFor Q14, see solution 884 at

Deletehttp://physics-ref.blogspot.com/2015/07/physics-9702-doubts-help-page-179.html

Explain June 2002 Paper 4 Q4c? Thanks

ReplyDeleteThe mass is no longer attached to the strip. So, as the strip moves up towards its highest point, the weight of the mass is no longer acting downwards against this motion. So, the amplitude is larger. Similarly, the strip moves quicker and thus, the period is shorter.}

Delete