Mock Exam Set 1 - Paper 1

A body moves a distance of 1.5 $km$ in 10 $ks$.

Which of the following gives the correct magnitudes of both of distance and time?

A student is using the equation $pV = nRT$ to solve for $n$ with the following percentage uncertainties in the measurements.

What is the percentage uncertainty in the calculated value of n?

• A. $\hspace{1em}$ 3 %

• B. $\hspace{1em}$ 7 %

• C. $\hspace{1em}$ 9 %

• D. $\hspace{1em}$ 12 %

An object is launched with an angle of $\theta$ from the ground and an initial velocity of $v$.

Which graph shows the variation of the horizontal component $v_h$ of the velocity of the object with time $t$? (Air resistance is not ignored)

A.			B.
		$\hspace{1cm}$
$\hspace{1em}$
C.			D.

An object is moving in a straight line. The graph shows the variation of the velocity $v$ of the object with time $t$.

Which of the following is correct according to the graph?

• I.	At point A, the object changes its direction.
  II.	At point C the object is at rest.
  III.	The magnitude of the acceleration at point D is greater than at point B.

• A. I only

• B. II only

• C. I and II only

• D. II and III only

A ball of mass $m$ is falling vertically through the air. The drag force acting on the ball is given by $kv^2$ where $k$ is constant and $v$ is the speed of the ball. What is the maximum speed reached by the ball?

• A. $\hspace{1em} \dfrac{k}{mg}$

• B. $\hspace{1em} \dfrac{mg}{k}$

• C. $\hspace{1em} \sqrt{\dfrac{k}{mg}}$

• D. $\hspace{1em} \sqrt{\dfrac{mg}{k}}$

A box of mass $3\, kg$ is placed on a box of mass $7\, kg$. The coefficient of static friction between the surfaces of the boxes is 0.5. A horizontal force $F$ is applied to the $7\, kg$ box which sits on a frictionless surface.

What is the maximum value of $F$ that can move the boxes without the $3\,kg$ box slipping?

• A. $\hspace{1em} 0.1g\,$

• B. $\hspace{1em} 0.5g\,$

• C. $\hspace{1em} g\,$

• D. $\hspace{1em} 5g\,$

A varying force acts on a spring. The variation of the extension $x$ of the spring with force $F$ acting on it is shown in the graph below.

The elastic potential energy stored in the spring is $E$ when the extension of the spring is $e$. What is the work done by force on the spring to increase the extension from $e$ to $3e$ ?

• A. $\hspace{1em} 2E$

• B. $\hspace{1em} 4E$

• C. $\hspace{1em} 8E$

• D. $\hspace{1em} 9E$

A box of mass $2.0\, kg$ starts to move on a level surface under the effect of a varying force $F$. The variation of $F$ with the displacement $s$ of the object is shown in the graph below.

What is the speed of the box at $s=5\, m$?

• A. $\hspace{1em} 5\,m\,s^{-1}$

• B. $\hspace{1em} \sqrt{5}\,m\,s^{-1}$

• C. $\hspace{1em} 15\, m\,s^{-1}$

• D. $\hspace{1em} \sqrt{15}\, m\,s^{-1}$

A trolley is pushed in a level parking area of a market on a very rainy day. The rain fills the trolley at a rate of $R\ {kg\,s}^{-1}$. Ignoring frictional forces, what is the force needed to move the trolley at a constant speed of $v$?

• A. $\hspace{1em} \ R v$

• B. $\hspace{1em} \dfrac{R}{v}$

• C. $\hspace{1em} \dfrac{v}{R}$

• D. $\hspace{1em} R+v$

A material with a mass of m is heated. The graph shows the variation of the temperature of the material with the energy supplied.

Which one of the following gives the specific heat capacity of the material?

• A. $\hspace{1em}$ $\dfrac{2Em}{T_2-T_1}$

• B. $\hspace{1em}$ $\dfrac{Em}{T_1}$

• C. $\hspace{1em}$ $\dfrac{2E}{m(T_2-T_1)}$

• D. $\hspace{1em}$ $\dfrac{E}{m(T_2-T_1)}$

100 ml of water at $20^oC$ is poured in an aluminum container and heated at a constant rate until all of the water is boiled. After time $t_1$ water starts to boil, and at time $t_2$ all of the water has boiled away.

Which of the following statements are correct?

• I.	If a glass container with the same mass is used instead of aluminum, $t_1$ increases. ($c_{\textrm{glass}} < c_{\textrm{aluminum}}$)
  II.	If the container with water is thermally isolated, $t_2$ decreases.
  III.	If more water is added to the container, $t_1$ increases.

• A. $\hspace{1em}$ Only I

• B. $\hspace{1em}$ I and II only

• C. $\hspace{1em}$ II and III only

• D. $\hspace{1em}$ I, II and III

An ideal gas is in a fixed volume container which sits on an electronic balance. More of the same gas is added to the container. Which of the following will not change?

• A. $\hspace{1em}$ The separation between the gas molecules

• B. $\hspace{1em}$ The collision frequency of the gas molecules with each other

• C. $\hspace{1em}$ The average size of the molecules

• D. $\hspace{1em}$ The reading on the electronic balance

The graph shows the variation with time $t$ of the displacement $s$ of an object suspended by a spring. At what time is the acceleration in the negative direction at a maximum?

• A. $\hspace{1em}$ 4.0 $s$

• B. $\hspace{1em}$ 3.0 $s$

• C. $\hspace{1em}$ 2.0 $s$

• D. $\hspace{1em}$ 1.0 $s$

A longitudinal wave is travelling in a medium from left to right. The graph shows the variation of the displacement of the particles of this medium with distance along the medium $x$.

Which point on the graph is at the center of a rarefaction? Displacements to the right of equilibrium positions are positive.

Two loudspeakers produce sound in phase of total intensity $I_0$ at point $A$

One of the loudspeakers is removed. The new intensity at point $A$ is now equivalent to:

• A. $\hspace{1em}$ $\dfrac{I_0}{4}$

• B. $\hspace{1em}$ $\dfrac{I_0}{2}$

• C. $\hspace{1em}$ $I_0$

• D. $\hspace{1em}$ $2I_0$

The diagram shows a beam of light passing from medium $X$ to medium $Y$.

If the angle of incidence of the light increases, which of the following changes can be implemented to keep the angle of refraction the same?

• I.	Medium X can be replaced with another medium which has a lower refractive index.
  II.	Medium X can be replaced with another medium which has a higher refractive index.
  III.	Medium Y can be replaced with another medium which has a higher refractive index.

• A. $\hspace{1em}$ Only I

• B. $\hspace{1em}$ I and III only

• C. $\hspace{1em}$ II and III only

• D. $\hspace{1em}$ I, II, and III

A student blows across the open end of a narrow cylinder which is closed at the other end. If the length of the cylinder is $15.0\,cm$ and the speed of sound is $340\,m\,s^{-1}$, What is the frequency of the wave at the third harmonic?

• A. $\hspace{1em}$ $1.1 \times 10^3\,Hz$

• B. $\hspace{1em}$ $1.7 \times 10^3\,Hz$

• C. $\hspace{1em}$ $2.8 \times 10^3\,Hz$

• D. $\hspace{1em}$ $3.4 \times 10^3\,Hz$

Estimate the speed of an alpha particle that has accelerated from rest in a uniform electric field $E = 50\,N\,C^{-1}$ over a distance of $2.0 \,m$.

• A. $\hspace{1em}$ $10^3 \ m \, s^{-1}$

• B. $\hspace{1em}$ $10^4 \ m \, s^{-1}$

• C. $\hspace{1em}$ $10^5 \ m \, s^{-1}$

• D. $\hspace{1em}$ $10^9 \ m \, s^{-1}$

A positive and a negative charge of equal magnitude are located on the same horizontal line.

What is the direction of the net electric field at the point marked X, equidistant from the two charges?

• A. $\hspace{1em}$ To the right

• B. $\hspace{1em}$ To the left

• C. $\hspace{1em}$ Up

• D. $\hspace{1em}$ Down

The circuit below consists of a cell and two identical resistors in parallel, with an ideal ammeter in one of the branches. The current in this branch is $I_1$ and the current in the other branch is $I_2$.

If the ideal ammeter is replaced by a real ammeter, what will be the effect on currents $I_1$ and $I_2$?

If the current in the circuit below is 0.5 $A$, what is the potential difference $V$?

• A. $\hspace{1em}$ 0.5 $V$

• B. $\hspace{1em}$ 10.5 $V$

• C. $\hspace{1em}$ 20.5 $V$

• D. $\hspace{1em}$ 40.5 $V$

An alpha particle of mass $m$ and charge $q$, is accelerated through a potential difference $V$ into a magnetic field of flux density $B$ that is at right angles to the direction of motion. Which of the sketches below best describes the relationship between the radius of path $r$ and the potential difference of the accelerating field?

A.			B.
		$\hspace{1cm}$
$\hspace{1cm}$
C.			D.

The tip of the seconds hand of a clock moves from the $\text{\textquotedblleft}$12$\text{\textquotedblright}$ marking to the $\text{\textquotedblleft}$6$\text{\textquotedblright}$ marking with a tangential speed of $2 \,cm \, s^{-1}$.

Which of the following is correct about the angular speed and the centripetal acceleration?

A proton and another object with charge +e exert electrical and gravitational forces on one another. To the nearest order of magnitude, what mass must the object have to be so that the net force acting on it is zero?

• A. $\hspace{1em} 10^1\,kg$

• B. $\hspace{1em} 10^3\,kg$

• C. $\hspace{1em} 10^6\,kg$

• D. $\hspace{1em} 10^9\,kg$

An electron in a hydrogen atom is excited from the ground state of $n=1$ to the $n=4$ level. What is the total number of frequencies that can be observed from the emission spectrum as the electron returns to ground state?

• A. $\hspace{1em}$ 12

• B. $\hspace{1em}$ 6

• C. $\hspace{1em}$ 4

• D. $\hspace{1em}$ 3

A 1.20 $kg$ sample of a radioactive isotope decaying via beta decay with a half-life of 30 minutes is observed in a closed container in a laboratory. The decay results in a daughter nucleus that is also a solid. What is the approximate total mass measured after 90 minutes?

• A. $\hspace{1em}$ 0.00 $kg$

• B. $\hspace{1em}$ 0.15 $kg$

• C. $\hspace{1em}$ 0.60 $kg$

• D. $\hspace{1em}$ 1.20 $kg$

Consider the following statements about nuclear binding energy:

The nuclear binding energy is:

• I. $\hspace{1em}$proportional to the mass defect from nucleus formation.
• II. $\hspace{0.7em}$the energy released when a nucleus is formed from its nucleons.
• III. $\hspace{0.4em}$the energy required to remove a proton from the nucleus.

Which of the statements are correct?

• A. $\hspace{1em}$ I only
• B. $\hspace{1em}$ I and II only
• C. $\hspace{1em}$ II only
• D. $\hspace{1em}$ I, II and III

Which of the following energy resources is non-renewable?

• A. $\hspace{1em}$ Biomass

• B. $\hspace{1em}$ Solar

• C. $\hspace{1em}$ Wind

• D. $\hspace{1em}$ Uranium-235

A thin metal plate of mass $m$ is held at an absolute temperature $T$, in an enclosure of temperature $T_s<T$ . One face of the plate has an area $A$. The temperature of the plate decreases by a small value $\Delta T$ in a short interval $\Delta t$, due to radiation. Assuming the metal plate to be a perfect black body, its specific heat capacity is given by:

• A. $\hspace{1em}$ $\dfrac{\sigma AT^4 \Delta t}{m(\Delta T)}$

• B. $\hspace{1em}$ $\dfrac{\sigma A(T^4-T_s\textrm{}^4 )\Delta t}{m(\Delta T)}$

• C. $\hspace{1em}$ $\dfrac{2\sigma AT^4 \Delta t}{m(\Delta T)}$

• D. $\hspace{1em}$ $\dfrac{2\sigma A(T^4-T_s\textrm{}^4 )\Delta t}{m(\Delta T)}$

A mass-spring system has a period of $T_0$. Another mass-spring system has a mass twice as large with a spring that requires four times as much force to obtain the same extension as the first system.

What is the new period in terms of $T_0$?

• A. $\hspace{1em} 2T_0$

• B. $\hspace{1em} \sqrt2T_0$

• C. $\hspace{1em} \dfrac{T_0}{\sqrt2}$

• D. $\hspace{1em} \dfrac{T_0}{2}$

Monochromatic light is incident from air on a set of thin films as shown. The first layer is used as a coating for the second layer. The refractive index of layer 1 is greater than the refractive index of layer 2. Layer 1 has negligible thickness. Two rays of light, $X$ and $Y$, are shown.

Which of the following is true for the phase difference and type of interference between $X$ and $Y$?

Light from a point source is incident on the pupil of the eye of an observer. The diameter of the pupil is $3.0 \,mm$.

What is the smallest angular separation of two distinct point sources of light, frequency $5.0 \times 10^8\, MHz$, that can be resolved by the observer?

• A. $\hspace{1em}$ 2.0 $\times 10^{-4}$ rad
• B. $\hspace{1em}$ 4.0 $\times 10^{-4}$ rad
• C. $\hspace{1em}$ 2.4 $\times 10^{-4}$ rad
• D. $\hspace{1em}$ 4.9 $\times 10^{-4}$ rad

A person is standing by the side of the road as a bus drives by. The bus emits a sound with a frequency of $f_0$ Hz. At a given instant, the frequency heard by the person is 10% percent higher than the emitted frequency. The speed of sound is 330 $m \, s^{-1}$.

Which of the following is correct for the speed of the bus and the direction of travel of the bus?

Equipotential lines representing the corresponding potentials are shown in the diagram, in an electric field.

Which of the following is a correct statement regarding this electric field?

• A. $\hspace{1em}$ The electric field is uniform.

• B. $\hspace{1em}$ The work done in moving an electron from P to Q is $20\, eV$

• C. $\hspace{1em}$ The work done in moving an electron from S to Q is $20\, eV$

• D. $\hspace{1em}$ The work done in moving an electron from R to S is $20\, eV$

The graph shows the variation of the total electric potential due to two point electric charges $q_1$ and $q_2$ located $4.0\, m$ apart. The distance $r$ is defined to be zero at the location of $q_1$.

What is the ratio of $\,\dfrac{q_2}{q_1}$ ?

• A. $\hspace{1em}$ 3

• B. $\hspace{1em}$ 4

• C. $\hspace{1em}$ 9

• D. $\hspace{1em}$ 16

The current $I$ in the conductor wire $X$ is decreasing which induces currents both in loops $Y$ and $Z$. The conductor wire and the loops lie in the same plane.

What is the direction of the induced currents in loop $Y$ and loop $Z$?