Explanation​:
To calculate $n$, the student would rearrange the formula to get

• n=PV/RT​

In both operations, the percentage uncertainty must be added, therefore the correct answer is C (2 % + 6 % + 1 % = 9 %)

Explanation​:
The distance is 1.5$km$ which is 1.5×10^3m, to convert it to $dm$, it will be $m$.

If we convert it to micrometers, it will be 1.5×10^9μm.

This eliminates answers A and D.

To convert the time from 10$ks$ to $ps$; it will be 10×10^15ps=10^16ps

therefore, the only correct answer for both of distance and time will be B.

Explanation​:
The change in velocity = final velocity - initial velocity = v2+(−v1), which can be represented as follows:

Explanation​:
Vectors of forces in equilibrium form a triangle or a straight line.
The sum of two sides of a triangle is always greater than the third (II is always true). The difference between two sides of a triangle is always less than the third (III is also always true).
I is true only when the three forces are in a straight line and FB​ and FC​ are both opposing FA​(not always true, as required by the question).

Explanation​:
The SI unit of power is W and it is defined as J s^−1.

Additionally, power can be calculated by
P = Fv
When units of force and speed are substituted in the equation, the units become
N m s^−1

But J is the SI unit of energy.
Therefore, the answer is B.

Explanation​:
In order for the plane to travel from $A$ to $B$, the resultant vector of the sum of the wind vector and the vector of the orientation of the plane must point in the same direction as the vector from $A$ to $B$, as shown in the diagram below. For any of the other choices, the resultant will not be in the direction $A$ to $B$.

Explanation​:
Impulse = change in momentum = $Ft$

So the magnitude of the change in momentum = (5.1×1035.1×103)(3.0) = 15300$Ns$

All responses match this quantity but the number of significant figures needs to be considered. As both of the values used in the calculation have two significant figures, there should be two significant figures in the answer.

In the answer $15000Ns$, the number of significant figures is unclear. It could be 2, 3, 4 or 5. The response $15kNs$ clearly has two significant figures, so it is the best answer

Explanation​:
Perimeter = 2(L+W)

uncertainty of perimeter will be calculated by adding the uncertainties of the four sides of the rectangle which gives (0.1+0.1+0.2+0.2)=0.6 cm

Explanation​:
In a decimal number, the zeroes to the left are not counted as significant figures, but the zeroes to the right are counted.

Therefore, the number of significant figures is 5 as only the bold part will be considered.

Explanation​:
The formula for potential energy stored is Ep=1/2kx^2

Since EP​ is calculated from multiplying $k$ and x^2 (ignoring the constant 1/2​ as there is no uncertainty for it), then the uncertainty of EP​ is calculated by adding the fractional uncertainties of x^2 and $k$.

The fractional uncertainty of x^2 is double the fractional uncertainty on x, which gives 2×3%=6%

The uncertainty of EP​ therefore = 2% + 6% = 8%

Explanation​:

sin 35o=vy/2​​

Therefore vy=2 sin(35o)

Explanation​:
The “Tare” button resets the balance display to zero. It avoids zero error when measuring weight with a container. It does not change the precision of the balance or the absolute uncertainty of the measurement. Without the use of the Tare button, all values will be wrong by the same amount, which is a systematic error.

According to Newton’s First Law, when the resultant force acting on the object is zero, the velocity of the object is constant. When head to tail method is applied to add the vectors of option C, the following is obtained.

The closed triangle represents a resultant force is zero.

Hence, the correct answer is C.

Explanation​:
The units for $k$ must be the unit of force divided by the unit of velocity, (kgms^−2/ms^−1​ ) therefore kgs^−1

Explanation​:
Leading zeros do not count in the number of significant figures (s.f.). Therefore, option A is 4 s.f.; option B is 3 s.f.; option C is 2 s.f.: option D is 1 s.f..

Explanation​:
To get the direction of the sum, we have to rearrange these vectors.

We can arrange them to start from the same point and complete the parallelogram, and then the diagonal from the starting point will be the sum vector.

Using any method will give the same direction of the vector, which is in the same direction as choice A.