__Physics__

1. A
ball A is thrown upfrom the edge of cliff and it lands below on the ground.
Another indentical ball B is thrown down from the cliff with the same velocity
as that of A. If the velocity of the ball A just before hitting the ground is v_{A}
and the velocity of B just before hitting the ground is v_{B} then

(a) **v _{A} = v_{B},** (b) v

2. Water
drips from the nozzle of a shower onto the floor 2m below. The drops fall at
regular intervals of time, the first drop striking the floor at the instant the
fourth drop begins to fall. What is the location of the second drop from the
floor? **8/9m**

3. Three
vectors , and are given. What is the value of 3C.(2A X B)? **540**

4. A person walks up a stalled 20m long escalator in 120s. When standing on the moving escalator he is carried up the same distance in 80 seconds. The time required to walk up the moving escalator is

(a) 24s (b) **48s** (c) 72s
(d) 96s

5. A passenger of mass 80Kg
stands on the floor of an elevator. If the elevator moves up with an
acceleration 2m/s^{2} then the normal reaction of the floor of the
elevator on the man is (assume g=10m/s^{2}) is

(a) 800N (b) 640N
(c) **960N** (d) 160N

6. A 10Kg monkey climbs up a massless rope that runs over a frictionless branch of a tree and back down to a 15Kg package on the ground. The magnitude of the least acceleration the monkey must have if it is to lift the package off the ground is

(a) 9.8m/s^{2} (b) 19.6m/s^{2} (c) **4.9m/s ^{2}** (d) 2.45m/s

7. A worker wishes to pile a cone of sand onto a circular area of radius 2m. The coefficient of static coefficient of friction between each layer of sand along the slope and the sand beneath it is 0.7 then assuming no slip the greatest height that the pile of sand can have is

(a) 2m (b) **1.4m** (c) 1m
(d) 0.7m

8. A
disc of mass 1kgslides along a circular path of radius 1m, on a frictionless table while attached to a
hanging block of mass 10kg through a hole in the table. The speed that can keep the block at rest is (assume g =
10m/s^{2})

(a) 1m/s (b) 5m/s
(c) **10m/s** (d) 20m/s

9. A
helicopter lifts a 70Kg diver from the sea by means of a cable 50m long. The
acceleration of the diver is g/20. How much work is done on the diver by the
force from the helicopter? (take g as 10m/s^{2}) **1750J**

10. The
force on a particle is directed along the x-axis and given by F = 240[(x/5)^{2}
– 1]. The work done by the force in moving the particle from x = 0 to x = 20 is

(a) 18.8kJ (b) 19.8kJ
(c) **20.8kJ** (d)21.8kJ

11. A
50Kg bungee cord jumper is on a cliff 50m high above a stream. The elastic
bungee cord has a relaxed length of 40m. The feet of the bungee jumper stops 2m
above the stream. Assume that the cord obeys Hooke’s law the spring constant of
the cord is (assume g = 10m/s^{2})

(a) 250N/m (b) 500N/m (c) **750N/m** (d) 1000N/m

12. A 5kg block is dropped from a height of 20cm onto a spring of force constant 2000N/m. The distance moved by the block after coming in contact with the spring is

(a) 5cm (b) **10cm** (c)15cm
(d)20cm

13. An object is placed on top of a hemispherical mound of ice of radius 6m. The object is given a small push after which it starts sliding. The height above the ground when the object leaves the hemispherical mound is

(a) 3m (b)
6m (c) 1m (d) **4m**

14. A 4kg block is placed on a horizontal surface and is connected to a spring of force constant 800N/m. The spring is compressed and then released. After the spring attains the relaxed length the block travels over the surface for a distance 10m. If the coefficient of kinetic friction for the surface is 0.4 the heat generated is

(a) 100J (b) 120J
(c)140J (d) **160J**

15. The coordinates of three masses 1kg, 3kg and 6kg are (1,1), (3,3) and (6,6) respectively. The coordinate of the centre of mass is

(a) (2,2) (b) (3,3) (c) (4,4)
(d) **(5,5)**

16. A rod strikes a stationary ball with an average force of 50N over a time of 10ms. If the ball has mass 0.2kg the speed of the ball after the impact is

(a) **2.5m/s** (b)
5m/s (c) 10m/s
(d) 20m/s

17. The
angular position of a point on a rotating wheel is given by θ = 2t^{2}
+ 4t +4. The angular velocity of the
point at t = 16s is

(a) 60rad/s (b)64rad/s (c) **68rad/s** (d)72rad/s

18. A
wheel of radius R is placed against a step of height h. If the mass of the
wheel is 10kg then the horizontal force required to be applied to the axle to lift
the wheel over the step assuming R = 2h is (take g = 10m/s^{2})

(a) **173N** (b)
273N (c)373N (d) 473N

19. Air
flows over the wing of an aircraft of area 50m^{2} with a speed 150m/s
and under the wing, also of the same area, with a speed 125m/s. If the density
of air is 1.25kg/m^{3} the upthrust on the wing is

(a) 0.415MN (b) 0.315MN (c) **0.215MN ** (d)
0.115MN

20. A block of mass 5kg is attached to two identical springs on either side of it. The springs are attached to the walls. The spring constant of the springs is 25N/m. The frequency of oscillation of the mass, when displaced from the equilibrium, is

(a) 2Hz
(b)
1Hz (c) **0.5Hz** (d) 0.25Hz

21. An acoustic burglar alarm has a source emitting waves of frequency 100Hz. When a stranger moves towards the alarm a beat frequency of 5Hz is detected. The speed of the stranger is (assume speed of sound as 330m/s)

(a) 6.04Hz (b) 7.04Hz (c) **8.04Hz** (d)9.04Hz

22. 10
moles of an ideal gas expand adiabatically from an initial temperature 100K to
a final temperature 200K. If C_{V} is the molar specific heat capacity
of the gas at constant volume the work done by the gas is

(a) 10C_{V} (b) 100C_{V} (c) **1000C _{V}** (d) 10000C

23. The
motor in a refrigerator has a power of 240W. The freezing chamber is at 290K
and the outside air is at 320K. What is maximum amount of energy that can be
extracted in 30min assuming that the refrigerator works as a Carnot cycle in
reverse? **40500J**

24. Two
small conducting balls of mass 50g and carrying a charge 10microcoulomb hang
from a thread of length 50cm. The separation between the balls at any instant
is (g =10m/s^{2})

(a) **1.2m**
(b) 1m (c) 0.8m (d) 0.6m

**25.
**A thin non conducting rod of length 1m has a
charge of 1C uniformly distributed over it. What is the electric field at a
point on the perpendicular bisector of the rod 0.5m from the centre? **24.5 x 10 ^{9}V/m**

26. Charge is distributed uniformly throughout the volume of an infinitely long cylinder of radius R with a charge density ρ. The electric field at a distance r (< R) cm from the axis of the cylinder is

(a)
**ρ
r/2ε _{0}** (b) ρ r/ε

27. A cylindrical capacitor has an internal radius r and external radius R. Half the stored electrical energy lies within a cylinder of radius

(a)
R+ r
(b) **(rR) ^{0.5}** (c) (R
-r) (d) (rR)

28. A wire L metres long is stretched to twice its length such that there is no change in the volume of the wire. If the wire earlier had a resistance R the new resistance of the wire is

(a)
R (b) 2R
(c) 3R (d) **4R**

29. When
a wire L metres long is turned into a circular coil the magnetic field at the
centre for a current I is B. The wire is wound into n turns. If the same
current passes through the coil what is the magnetic field at the centre of the
coil? **100B**

30. Two long parallel wires of equal radius R are placed a distance r apart. If they carry equal currents in opposite directions then the inductance per unit length of the pair of wires is

(a)
**(μ _{0}/π)(ln(r
– R)/r** (b) (μ

31. The optical path length of a ray of light in vacuum is 2cm. The optical path length in a medium of refractive index 2 is

(a)
1cm
(b) **4cm** (c) 2cm (d) 0

32. A source and a screen are a distance 10cm apart. If the focal length of the lens is 2cm then two real images are formed for lens position separated by

(a)
2.24cm
(b) **4.48cm** (c) 6.72cm (d) 8.96cm

33. A glass lens is coated on one side with a thin film of magnesium fluoride whose refractive index is 1.38. if the refractive index of glass is 1.5 what is the least thickness that eliminates reflections at 550nm

(a)
50nm
(b) **100nm** (c)150nm (d)200nm

34. The
wavelength associated with the cutoff frequency for a metal is 300nm. What is
the maximum kinetic energy of electrons ejected from the metal surface by UV
light of wavelength 250nm? **0.82eV**

35. A 1.00g sample of Samarium (Sm) emits alpha particles at a rate of 120 particles/s. The isotope responsible for the decay is Sm - 147 has a natural abundance in bulk samarium of 15%. The half life for the decay process is

(a)
10^{9} y (b)
10^{10} y (c) **10 ^{11}
y** (d) 10