clicked correct time. Re is the radius of Earth. e
linear coe cient of the material of pendulum is
(a) h
Re
(b) h
5 Re
(c)^5 R
h
e (d) R
h
e
- Two particles move parallel to x-axis about the
origin with same amplitude 'a' and frequency Z. At a
certain instant they are found at a distance a/3 from
the origin on opposite sides but their velocities are
in the same direction. What is the phase di erence
between the two?
(a) cos−^1
7
9
(b) cos−^1
5
9
(c) cos−^1
4
9
(d) cos−^1
1
9
- Two loudspeakers are emitting sound waves of
wavelength O with an initial phase di erence of p/2.
At what minimum distance from O on line AB will
one hear a maxima?
(a) 25 O
(b)
100
15
λ
100 O
O
A
B
3 O
(c)
25
3
λ
(d) 50 O
- A rod is arranged at an angle of 30° from the
horizontal. Attached to the rod with two strings
is the mass m, as shown. e rod is rotated,
maintaining its direction in space, so that m travels
in a circular path. e strings are of equal length,
and make angles of 60° with the rod as shown. Take
the length of the strings as 2.4 m. Calculate the
minimum value of the tangential speed (in m s–1) of
the mass such that the string with tension T 2 does
not becomes slack when the mass directly above the
rod.
(a) 6
(b) 0.2
60°
60°
T 2 T^1
30°
Side view
(c) 6 m
(d) 2.7
- An electron of mass me, initially at rest, moves
through a certain distance in a uniform electric eld
in time t 1. A proton of mass mp, also initially at rest,
takes time t 2 to move through an equal distance in
this uniform electric eld. Neglecting the e ect of
gravity, the ratio of t 2 /t 1 is nearly equal to
(a) 1 (b) (mp/me)1/2
(c) (me/mp)1/2 (d) 1836
14. In the circuit shown in g the heat produced in the
5 ohm resistor due to the current owing through it
is 10 calorie per second. e heat generated in the
4 ohm resistor is
(a) 1 cal s–1 (b) 2 cal s–1
(c) 3 cal s–1 (d) 4 cal s–1
15. A potential di erence of 500 V
is applied across the plates
of a parallel plate condenser.
e separation between the
plates is 3 mm. An electron
projected vertically, parallel to
the plates, with a velocity of
3 × 10^6 m s–1 moves undeected
between the plates.
Find the magnitude of the magnetic eld in the
region between the condenser plates. (Neglect the
edge e ects).
(Charge of the electron = – 1.6 × 10–19 coulomb)
(a) 0.055 T (b) 0.83 T (c) 1.49 T (d) 3.58 T
16. A proton, a deuteron and an D-particle having
the same kinetic energy are moving in circular
trajectories in a constant magnetic eld. If rp, rd and
rD denote respectively the radii of the trajectories of
these particles, then
(a) rD = rp < rd (b) rD > rd > rp
(c) rD = rd > rp (d) rp = rd = rD
17. A coil of inductance 8.4 mH and resistance 6 : is
connected to a 12 V battery. e current in the coil
is 1.0 A at approximately the time
(a) 500 s (b) 25 s (c) 35 ms (d) 1 ms
18. A ray of light is incident at an angle of 60º on one
face of a prism which has an angle of 30º. e
ray emerging out of the prism makes an angle of
30º with the incident ray. e emergent ray is
perpendicular to the face through which it emerges
calculate the refractive index of the material of the
lens.
(a) 3 (b) 5 (c) 7 (d)^14
19. A telescope has an objective of focal length 50 cm
and an eyepiece of focal length 5 cm. e least
distance of distinct vision is 25 cm. e telescope
is focussed for distinct vision on a scale 200 cm
away from the objective. Calculate the separation
between the objective and the eyepiece
(a) 70.8 cm (b) 88 cm
(c) 95 cm (d) 109 cm
+ + + + + + +
500 V
