1. Two objects A and B are separated by a distance $r$. The mass of A is much larger than that of B.

Which of the following is correct about magnitude and direction of the gravitational force exerted by A on B compared to that exerted by B on A?

2. Two point charges are separated by a distance $r$ as shown.

3. Estimate the speed of an alpha particle that has accelerated from rest in a uniform electric field E=50NC^−1 over a distance of 2.0m.

4. 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?

5. A plastic rod carrying a uniformly distributed positive charge is bent into a quarter-circle. What is the direction of the electric field at point $P$?

6. The diagram below shows a circuit connected to an iron rod $XY$. The connecting wires are flexible. The rod is placed in a magnetic field directed perpendicularly into the page as shown.

In what direction will the resultant force act on the rod when the current is switched on in the circuit?

7. A current-carrying wire is at right angles to a uniform magnetic field. The magnetic force per unit length on the wire is F/L. The length of the wire, the magnitude of the magnetic field strength, and the current of the wire are all doubled. Which of the following is the magnetic force per unit length on the wire after these changes?

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?

8.

A.			B.
C.			D.

9. Satellites $A$ and $B$ orbit the same planet of mass $M$. Satellite $A$ has a mass of $3m$ and it is located at a height of $R$ from the surface of the planet. Satellite $B$ has a mass of $m$ and it is located at a height of 2$R$ from the surface of the planet.

What is the ratio of the centripetal force acting on $A$ to the centripetal force acting on $B$?

10. Which of the following correctly lists the fundamental forces in decreasing order of strength?

11. Two charges separated by a distance $r$ are placed in a medium with permittivity $ϵ$. The charges are then moved to air so that they have the same force between them as that in the medium.

12. The centers of three masses lie on the same line. The centers of the masses are separated as shown.

The net gravitational force on m2 is zero when the value of $d$ is one third of $x$. What is the ratio m1/m3?

13. Planet $A$ has a gravitational field strength $g$ at its surface. Planet $B$ has twice the density and twice the radius of planet $A$.

What is the gravitational field strength at the surface of $B$?

14. A beam of electrons enters a uniform electric field, as shown.

What effect does this field have on the horizontal and vertical components of the electrons' velocity?

15. The gravitational field strength on the surface of the moon is gE/6. Two objects of different masses $m$ and $2m$ are released with zero speed on the moon from heights of $h$ and $2h$, respectively, where $h$ is small compared to the radius of the moon.

What are the magnitudes of the accelerations of these objects right after release?

16. An object of mass $m$ and charge $q$ is dropped vertically between two parallel plates, $K$ and $L$. A magnetic field $B$ can be created perpendicular to the plane of the paper. The electric field between plates is $E$.

Which of the following is correct about the magnitude of magnetic and electric fields when the object falls vertically at a constant velocity v?

17. Satellite $A$ of mass $M$ orbits a planet with an orbital speed $v$ and orbital radius $R$. Another satellite $B$ with mass $3M$ orbits the same planet with the same orbital speed.

18. A wire is carrying a current $I$ is placed in a region of uniform magnetic field B1. The magnitude of the magnetic field is $B$, and its direction is into the page. The force acting on the wire is $F$, as shown in the diagram.

The wire, carrying the same current $I$, is now placed with the orientation shown into another region of uniform magnetic field B2. The magnitude of the magnetic field is $B$, and its direction is out of the page.

What is the correct direction and magnitude of the force acting on the wire in field B2?

	Direction	Magnitude
A.		$F$
B.		$F$
C.		$F\sin \theta$
D.		$F\sin \theta$

19. Two stars of equal mass $M$ are shown in the diagram, distance $d$ apart. A planet is equidistant from the two stars, with distance d/2 across the midpoint of the line joining the stars as shown.

What is the resultant gravitational field strength at the position of the planet due to the two stars?

20. Two charges, separated by a large distance, are shown below, along with the electric field lines around each charge.

Which of the following statements is correct?

• I.  The charge $q$ is positive.
• II.  The charge $q$ is equal in magnitude to $+Q$.
• III.  The electric field magnitude near the charge $q$ is greater than the magnitude of the field near the charge $+Q$.

21. In the following diagram, the size of the charges is small compared to the distance R.

What is the direction of the force on the charge in the center?

22. A satellite is in a circular orbit of radius $R$ around a planet of mass $M$. Which of the following graphs represents the relationship between the centripetal acceleration of the satellite and its orbital radius?

A.				B.
C.				D.

23. Planet $X$ has radius $R$ and density $\rho$. The gravitational field strength at the surface of Planet $X$ is $g$.

What is the ratio of the gravitational field strength at the surface of planet Y, which has radius 0.25$R$ and density 3$\rho$, to that at the surface of Planet X?

24. A source of radiation is near a magnetic field that is directed into the page. A sheet of paper is placed in the path of the radiation before it enters the magnetic field.

The gamma radiation is not deflected when entering the magnetic field. Which of the following is correct about the other type of radiation that penetrates the paper sheet and the direction of its deflected path in the magnetic field?

25. Two positive charges q1 and q2 are separated by a distance $d$. A third positive charge $q$ is placed at a distance d/4 from q1 so that the charge $q$ is in equilibrium.

What is the ratio q1/q2?