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 fundamental SI units?

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

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 vector quantities?

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

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 

The vectors below represent the displacement of two cars.

What is the direction of S_{A}-S_{B}?

Question 7 

An object of mass 0.0250 kg starts accelerating from rest and reaches a speed of 25.82 m s^{-1}. What is the change in the kinetic energy of the object?

1. 8 J
2. 8.3 J
3. 8.33 J
4. 8.333 J

Question 8 

Which of the following is a vector quantity?

1. Electric current
2. Distance
3. Pressure
4. Electric field strength

Question 9 

A person swims across a river that is flowing east. In what direction does the person have to swim so that she only moves towards the south from her starting point?

Question 10 

Which of the following is a fundamental SI unit?

1. Ampere
2. Joule
3. Newton
4. Coulomb

Question 11 

Which of the following answer options has two vector and two scalar quantities?

1. Force, momentum, mass, acceleration
2. Kinetic energy, velocity, potential difference, displacement
3. Speed, potential energy, temperature, current
4. Charge, impulse, power, time

Question 12 

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

Question 13 

The radius of a spherical planet is X and the absolute uncertainty in the radius of the planet is \Delta X. What is the fractional uncertainty in the volume of the planet?

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

Question 14 

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 15 

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 16 

Which of the following answer options includes three scalar quantities?

1. Mass, speed, weight, magnetic field strength
2. Acceleration, time, temperature, velocity
3. Electric current, electric field strength, displacement, charge
4. Gravitational potential energy, amplitude, momentum, power

Question 17 

The charge of a proton is:

1. 1.60 \times 10^{-34} PC
2. 1.60 \times 10^{-22} mC
3. 1.60 \times 10^{-13} MC
4. 1.60 \times 10^{-4} pC

Question 18 

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 19 

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 20 

The side length of a cube is 20 \pm 5 cm. What is the absolute uncertainty in the volume of the cube?

1. 125 cm^{3}
2. 625 cm^{3}
3. 6000 cm^{3}
4. 8000 cm^{3}

Question 21 

A biker travels at a constant speed of 8 m s^{-1} west during a minute and then at a constant speed of 6 m s^{-1} south during a minute. What is the average speed of the biker during these two minutes?

1. 5 m s^{-1}
2. 7 m s^{-1}
3. 10 m s^{-1}
4. 14 m s^{-1}

Question 22 

An apple is released from rest near the surface of the Earth. It hits the ground after 2 s. What is the best estimate for the apple’s momentum right before it hits the ground?

1. 3 \times 10^{0} kg m s^{-1}
2. 3 \times 10^{1} kg m s^{-1}
3. 3 \times 10^{2} kg m s^{-1}
4. 3 \times 10^{3} kg m s^{-1}

Question 23 

The time it takes for light to cross a helium nucleus is approximately:

1. 10^{-7} s
2. 10^{-15} s
3. 10^{-21} s
4. 10^{-23} s

Question 24 

A student carries out an experiment to determine the speed of a toy car. The results of the experiment are shown on the graph. 

What is true about the random and the systematic errors in the student’s data?

Question 25 

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

Which vector represents Y – X?

Question 26 

Which of the following units is equivalent to W m^{-1}?

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

Question 27 

A block of mass m is sliding down a frictionless slope. The angle that the slope makes with the horizontal is \beta. 

The normal reaction force that acts on the block is R. What is the resultant force on the block?

1. mgsin\beta
2. mgcos\beta
3. Rsin\beta
4. Rcos\beta

Question 28 

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 29 

A force of 10 N can be resolved along directions AB and AC, where AB and AC are perpendicular to each other. 

The component of the force in the AC direction is 6 N. What is the magnitude of the component along the AB direction?

1. 2 N
2. 4 N
3. 6 N
4. 8 N

Question 30 

Work done per unit volume has the same units as:

1. Impulse
2. Specific energy
3. Force
4. Pressure

Question 31 

A student measures the base of a triangle as 20 \pm 1 cm and its height as 8 cm \pm 4 %. What is the fractional uncertainty in the area of the triangle?

1. \frac{1}{20}
2. \frac{9}{100}
3. \frac{51}{100}
4. \frac{11}{20}

Question 32 

The fundamental SI unit combination for volt is:

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

Question 33 

Two perpendicular forces of magnitudes 9 N and 12 N act on an object. The magnitude of the resultant force on the object is:

1. 3 N
2. 11 N
3. 15 N
4. 21 N

Question 34 

A point charge is placed in an electric field. The uncertainty in the electric force that acts on the point charge is 8 % and the uncertainty in the charge of the point charge is 4 %.  What is the percentage uncertainty in the electric field strength?

1. 2 %
2. 4 %
3. 12 %
4. 32 %

Question 35 

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 36 

The best estimate for the order of magnitude of the ratio \frac{electron \:  rest \: mass}{neutron \:  rest \:  mass} is:

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

Question 37 

The side length of a cube is 50 \pm 1 cm and its mass is 60 \pm 3 kg. What is the percentage uncertainty in the density of the cube?

1. 4 %
2. 7 %
3. 11 %
4. 13 %

Question 38 

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 39 

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 40 

The mass of a car is 1000 kg \pm 5 % and its kinetic energy is 200 kJ \pm 15 %. What is the absolute uncertainty in the speed of the car?

1. 0.6 m s^{-1}
2. 1 m s^{-1}
3. 2 m s^{-1}
4. 4 m s^{-1}

Question 41 

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 42 

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 43 

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 44 

Three forces with magnitudes A, B, and C lie in the same plane and act on an object. The object is in equilibrium. 

Which of the following equations is correct?

1. A = B + C
2. Asin\alpha = B
3. Csin\alpha = A - Bcos\alpha
4. Acos\alpha = C

Question 45 

The period of a mass-spring system that oscillates with simple harmonic motion (SHM) can be calculated using the formula T = 2 \pi \sqrt{\frac{m}{k}} where T is the period of the oscillations, m is mass and k is the spring constant. The percentage uncertainty in the period is 4 % and the percentage uncertainty in the mass is 8 %. What is the percentage uncertainty in the spring constant?  

1. 0.5 %
2. 1 %
3. 16 %
4. 24 %

Question 46 

A cube-shaped container is filled with 1000 litres of water. The density of water 1 g cm^{-3}. The difference in the orders of magnitude of the diameter of a water molecule and the side length of the container is:

1. 14
2. 12
3. 10
4. 8

Question 47 

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 48 

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 49 

The graph shows a data set from an experiment. 

What is the percentage uncertainty in the vertical axis intercept of the line of best fit for the data set?

1. 30 %
2. 50 %
3. 70 %
4. 100 %

Question 50 

The radius of a sphere is measured to be 10 \pm 1 cm. What is the best estimate for the absolute uncertainty in the volume of the sphere?

1. 1 cm^3
2. 12 cm^3
3. 100 cm^3
4. 1200 cm^3

Question 51 

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

Question 52 

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 53 

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 54 

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 55 

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