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Physics S Paper

1. The uncertainty u in the measurement of the speed of a wave v is given by u = 0.005v + 4/v. What is the speed v which has the least uncertainty? (Round off to the nearest integer; DO NOT type in the units; just type the number)

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2. Which of the following comprises one vector and one scalar quantity?

Torque, Acceleration
Magnetic Field, Magnetic Flux Density
Magnetic Flux, Electric Field
Angular Velocity, Momentum

3. A ball drops from a height of 9 m. Each time it hits the ground, it loses 20% of its kinetic energy. What is the total distance travelled by the ball before it comes to rest?

73 m
81 m
95 m
105 m

4. A ball of mass M travelling at speed u makes a head on elastic collision with another ball of mass m which is initially at rest. What is a correct expression for the velocity of the second ball (of mass m) after the collision?

2u/(m/M + 1)
2u/(M/m + 1)
2u/(m + 1/M)
2u/(M + 1/m)

5. A beaker half-filled with water is placed at the centre of a rotating table which is rotating with a period of 0.5 s. What is the equation of the parabola that describes the shape of the water surface?

y = 4 x-squared
y = 8 x-squared
y = 16 x-squared
y = 32 x-squared

6. What is the gravitational potential at the centre of the Earth, in terms of the gravitational constant G, its density d, radius R and pi (3.1416)?

-2(pi)GdR/3
-4(pi)GdR/3
-(pi)GdR
-2(pi)GdR

7. Estimate the root-mean-square speed of an oxygen molecule at room temperature at sea level.

60 m/s
120 m/s
240 m/s
480 m/s

8. If the ratio Pt/Ptr is 2.5 when Ptr is 100 kPa; and 2.3 when Ptr is 80 kPa, what is the temperature of the gas?

409.74 K
394.68 K
328.71 K
273.16 K

9. In an adiabatic process for air, pV^1.403 = constant. Air at 20 Degree Celsius and 1 atmospheric pressure is compressed adiabatically to 1/10 of its original volume. What is its final temperature?

741 K
662 K
589K
498 K

10. A spring-mass system comprises two springs connected in series, one above the other. The spring constants of the two springs are k1 and k2. A mass m is suspended at the bottom of the lower spring. What is its natural period of oscillation?

2(pi)(m(k1 + k2)/k1k2)^½
2(pi)(mk1k2/(k1 + k2))^½
2(pi)(m/(k1 + k2)k1k2)^½
2(pi)(m(k1 + k2)k1k2)^½

11. Light from a sodium lamp comprising two wavelengths 589.0 nm and 589.6 nm falls normally on a diffraction grating with 560 lines per mm. If the diffracted rays have to be separated by at least 0.1 Degrees, which order could be used?

1
2
3
4

12. Given that the electric field strength near a surface is equal to the ratio of its surface charge density to permittivity of free space, estimate the electric field strength at the surface of a lamp post 10 m tall, with a trunk cross-sectional area of 700 cm-squared, and given a charge of 0.05 mC.

500 V/m
8,000 V/m
40,000 V/m
600,000 V/m

13. A variable capacitor set at C is connected in parallel with a fixed capacitor of value C. Both are connected in parallel with a battery of e.m.f. Vo, and then disconnected. Thereafter, the variable capacitor is adjusted so that its capacitance becomes 0.5 C. What is the new p.d. across the capacitors?

1.33 Vo
1.67 Vo
2.33 Vo
2.67 Vo

14. Superman participates in a rope-skipping competition. He uses a 3 m long steel wire and skips 3,000 times per second. Assuming he is facing North and the Earth's horizontal magnetic field is 0.00002 T, what is the peak value of the e.m.f. between the two ends of the rope? (Assume the rope forms a semi-circle while he is skipping)

0.54 V
8.25 V
31.2 V
563 V

15. If all the following voltage waveforms have the same peak value Vo and are connected across the same resistance, what is the ratio of the power dissipated in a d.c. : sinusoidal : sawtooth wave?

1 : 2 : 3
3 : 2 : 1
6 : 3 : 2
6 : 2 : 3

16. A magnetic field of strength 8 mT is directed towards the positive x-axis. An electron travelling at 200,000 m/s enters this magnetic field at an angle of 30 Degrees to the positive x-axis. What is the pitch of the electron's helical path?

0.32 mm
0.45 mm
0.77 mm
0.89 mm

17. In an electron diffraction experiment, the angle of diffraction is 0.2 rad. If the accelerating potential of the electron beam is doubled, what is an approximate value of the angle of diffraction?

0.05 rad
0.07 rad
0.14 rad
0.40 rad

18. A satellite observatory observes the Hydrogen absorption spectrum of light from the Sun. Due to re-radiation of the absorbed energy, the dark lines' intensity is not completely zero. If cool hydrogen vapour is now inserted between the sunlight and the diffraction grating, what change, if any, will happen to the absorption spectrum.

Nothing.
The U.V. band's intensity drops
The Visible band's intensity drops
The Infrared band's intensity drops

19. An approximate formula for the radius of a nucleus is R = (1.2 x 10^-15) A^1/3 where A is the nucleon or mass number. What is the likely ratio for the radius of a Plutonium nucleus (atomic number 94) to that of a Helium nucleus (atomic number 2)?

1.0
1.2
3.6
3.9

20. A source contains two radioactive nuclides A and B. The half-life of A is 14 days and that of B is 21 days. At time t = 0, 90% of the decay came from A. What time has elapsed before 90% of the decay comes from B?

266 days
298 days
363 days
382 days


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