Question

Two steel wires P and Q have lengths 1 and 21 respectively, and cross sectional areas A and A/2
respectively. Both wires obey Hooke's law

What is the ratio of
tension in P /Tension in Q
when both wires are stretched to the same extension
a.1/4

b.1/2

c2/1

d4/1​

Answer 1

Answer:

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.