Black Hole

Basic

Moderate

Challenging

Difficult

Black Hole

Question 1 

The number of significant figures in 0.02670 is:

1. 3
2. 4
3. 5
4. 6

Question 2 

Which of the following are two vector quantities?

1. Speed, Mass
2. Speed, Force
3. Velocity, Mass
4. Force, Velocity

Question 3 

Repeating readings in an experiment reduces:

1. Both random and systematic errors
2. Random errors only
3. Systematic errors only
4. Neither random, nor systematic errors

Question 4 

Which of the following are two fundamental SI units?

1. mole, kelvin
2. ampere, pascal
3. joule, meter
4. second, newton

Question 5 

A ball of 0.18 kg is traveling at a speed of 3.210 m s^{-1}. The mass and the velocity of the ball are used to calculate the magnitude of its momentum. What is the correct number of significant figures for the magnitude of the ball’s momentum?

1. 2
2. 3
3. 4
4. 5

Question 6 

What is the unit of pressure in fundamental SI units? 

1. N m^{-1}
2. N m^{-2}
3. kg m^{-1} s^{-2}
4. kg m^{-2} s^{-2}

Question 7 

A particle is moving upwards in a straight line at constant speed. Which diagram represents the forces acting on this particle?

Question 8 

Which of the following quantities has the fundamental SI unit combination of kg m s^{-1}?

1. Power
2. Energy
3. Impulse
4. Force

Question 9 

The side length of a square is measured to be y \pm \Delta y. What is the fractional uncertainty in the area of the square?

1. \frac{\Delta y}{y}
2. \frac{2 \Delta y}{y}
3. \frac{\Delta y}{2y}
4. \left ( \frac{\Delta y}{y} \right )^{2}

Question 10 

What is the order of magnitude, in cm, of an adult human being who has an average height?

1. -1
2. 0
3. 1
4. 2

Question 11

The mass of a car is 1000 kg\pm5% It is moving at a constant speed of 30.0 m s^{-1}\pm3%. What is the percentage uncertainty in the kinetic energy of the car?

1. 8 %
2. 11 %
3. 14 %
4. 45 %

Question 12

Which of the following is a unit of acceleration?

1. J kg^{-1} m^{-1}
2. N kg^{-1} m^{-1}
3. J kg m^{-1}
4. N kg m^{-1}

Question 13

What is the size of a carbon nucleus?

1. 0.0027 fm
2. 0.0027 pm
3. 0.0027 nm
4. 0.0027 \mum

Question 14

Two forces, X and Y, are represented by the following vectors:

Which vector represents Y – X?

Question 15

The mass of an object is 5.0 \pm 0.1 kg and its speed is 20 \pm 1 m s^{-1}.

What is the percentage uncertainty in the kinetic energy of the object?

1. 6%
2. 7%
3. 12%
4. 25%

Question 16

Two masses, X and Y, are 62\pm2 kg and 28\pm1 kg respectively. Which of the following has the largest fractional uncertainty?

1. 2X + Y
2. X – 2Y
3. \frac{3Y}{X}
4. 4XY

Question 17

A coal-fired power plant uses 9 \times 10^{6} kg of coal per day. All the coal that is used in the power plant is composed of carbon-12 atoms. 

What is the best estimate for the number of carbon-12 atoms used per month in the power plant?

1. 10^{9}
2. 10^{24}
3. 10^{31}
4. 10^{34}

Question 18

A student carries out an experiment to examine how the kinetic energy of an object varies with the speed of the object. The results are shown on the graph.

What can be deduced about the type of errors in the student’s measurements?

Question 19

A stone is thrown with initial velocity v at an angle \theta to the horizontal. The magnitude of the vertical component of the stone’s velocity is 10 m s^{-1}. 

What is the value of \theta?

1. sin^{-1}\left ( \frac{10}{v} \right )
2. sin^{-1}\left ( \frac{v}{10} \right )
3. cos^{-1}\left ( \frac{10}{v} \right )
4. cos^{-1}\left ( \frac{v}{10} \right )

Question 20

A box is in the shape of a rectangular prism. The length, width and height of the box are measured to be 5 cm, 10 cm, and 20 cm respectively. The uncertainty in each measurement is \pm 1 cm.

What is the absolute uncertainty in the volume of the box?

1. 3.5 cm^{3}
2. 100 cm^{3}
3. 350 cm^{3}
4. 500 cm^{3}

Question 21 

The volume of a cone is 30\pi \pm 0.9 \pi cm^{3} and its height is 100 \pm 7 mm. The volume of a cone can be calculated using V = \frac{1}{3} \pi r^{2} h where V is volume, r is radius and h is height. 

What is the absolute uncertainty in the diameter of the cone?

1. 0.01 m
2. 0.005 m
3. 0.003 m
4. 0.002 m

Question 22 

Three forces, \overrightarrow{A}, \overrightarrow{B} and \overrightarrow{C}, act on object X as shown on the diagram. Object X moves at constant velocity. 

Consider the following three equations:

I. \overrightarrow{A} + \overrightarrow{B} = - \overrightarrow{C}

II. \left | \overrightarrow{B} \right |cos(\alpha) = \left | \overrightarrow{C} \right |cos\left ( \frac{\pi}{2} - \alpha \right )

III. \left | \overrightarrow{A} \right | = \left | \overrightarrow{B} \right |sin(\alpha) + \left | \overrightarrow{C} \right |cos(\alpha)

Which of these three equations are correct?

1. I and II only
2. I and III only
3. II and III only
4. I, II and III

Question 23 

A stone is attached to a metal rod and rotated in a horizontal circle. The centripetal acceleration, a, of the stone is measured for different rotational time periods, T. 

Given that random errors were minimised during the experiment, which of the following graphs will have a straight line of best fit?

1. a against T^{2}
2. a^{2} against T
3. a against T^{-2}
4. a^{-2} against T

Question 24 

Two quantities, x and y, are related as shown on the graph. The vertical axis intercept of the graph is c and the gradient of the graph is \frac{1}{m}.

Which of the following equations correctly shows the relationship betweenx and y?

1. c = y - mx
2. c = my - x
3. x = my - c
4. x = my - mc

Question 25 

In an experiment, the following values are measured and given together with their uncertainties:

a = 2.0 \pm x

b = 16 \pm 2%

c = 0.50 \pm 0.07

Then, H is calculated using the formula H = \frac{3a^{3}}{2 \sqrt{b} \times c}. For the values given above, the absolute uncertainty in H is \pm 1.8.

What is the value of x?

1. 0.1
2. 0.2
3. 0.3
4. 0.4