Best Question on Jee physics

ONLY ONE OPTION IS CORRECT.
Take approx. 2 minutes for answering each question.

Q.1 A wave is propagating along x-axis. The displacement of particles of the medium in z-direction at t = 0
is given by: z = exp[ –(x + 2)2] , where ‘x’ is in meters. At t = 1s, the same wave disturbance is given by:
z = exp[ – (2 – x)2 ]. Then, the wave propagation velocity is
(A) 4 m/s in + x direction (B) 4 m/s in –x direction
(C) 2 m/s in + x direction (D) 2 m/s in – x direction
Q.2 The equation of a wave travelling along the positive x-axis, as shown in
figure at t = 0 is given by
   
   kx  t         
(A) sin  kx  t   (B) sin  6 (C) sin   t  kx   (D) sin t kx
 6   6   6 
Q.3 Figure shown the shape of part of a long string in which
transverse waves are produced by attaching one end of the
string to tuning fork of frequency 250 Hz. What is the velocity
of the waves?
(A) 1.0 ms–1 (B) 1.5 ms–1
–1
(C) 2.0 ms (D) 2.5 ms–1
Q.4 A block of mass 1 kg is hanging vertically from a string of length 1 m and
mass/length = 0.001 Kg/m. A small pulse is generated at its lower end. The pulse
reaches the top end in approximately
(A) 0.2 sec (B) 0.1 sec (C) 0.02 sec (D) 0.01 sec
Q.5 A uniform rope having some mass hanges vertically from a rigid support. A transverse wave pulse is
produced at the lower end. The speed (v) of the wave pulse varies with height (h) from the lower end as:



(A) (B) (C) (D)


Q.6 A wire of 10–2 kgm–1 passes over a frictionless light pulley fixed on the top of a frictionless inclined plane
which makes an angle of 30° with the horizontal. Masses m and M are tied at two ends of wire such that
m rests on the plane and M hangs freely vertically downwards. The entire system is in equilibrium and a
transverse wave propagates along the wire with a velocity of 100 ms–1.
m 1 m
(A) M = 5 kg (B) = (C) m = 20 kg (D) =4
M 4 M
Q.7 A pulse shown here is reflected from the rigid wall A
and then from free end B. The shape of the string
after these 2 reflection will be

(A) (B)


(C) (D)

, Q.8 A composition string is made up by joining two strings of different masses per unit length  and 4.
The composite string is under the same tension. A transverse wave pulse : Y = (6 mm) sin(5t + 40x),
where ‘t’ is in seconds and ‘x’ in meters, is sent along the lighter string towards the joint. The joint is at
x = 0. The equation of the wave pulse reflected from the joint is
(A) (2 mm) sin(5t – 40x) (B) (4 mm) sin(40x – 5t)
(C) – (2 mm) sin(5t – 40x) (D) (2 mm) sin (5t – 10x)
Q.9 In the previous question, the percentage of power transmitted to the heavier string through the joint is
approximately
(A) 33% (B) 89% (C) 67% (D) 75%
Q.10 A wave pulse on a string has the dimension shown in figure. The waves
speed is v = 1 cm/s. If point O is a free end. The shape of wave at time
t = 3 s is :



(A) (B) (C) (D)

Q.11 A string 1m long is drawn by a 300Hz vibrator attached to its end. The string vibrates in 3 segments.
The speed of transverse waves in the string is equal to
(A) 100 m/s (B) 200 m/s (C) 300 m/s (D) 400 m/s
Q.12 A wave is represented by the equation y = 10 sin 2(100t0.02x) + 10 sin 2(100t+0.02x).
The maximum amplitude and loop length are respectively
(A) 20 units and 30 units (B) 20 units and 25 units
(C) 30 units and 20 units (D) 25 units and 20 units
Q.13 The resultant amplitude due to superposition of two waves y 1 = 5sin (wt  kx) and
y2 = 5 cos (wt  kx 150°)
(A) 5 (B) 5 3 (C) 5 2  3 (D) 5 2  3
Q.14 A wave represented by the equation y = A cos (kx –t) is superimposed with another wave to form a
statioary wave such that the point x =0 is a node. The equation of the other wave is:
(A) –A sin (kx +t) (B) – A cos (kx + t) (C) A sin (kx + t) (D) A cos (kx + t)
Q.15 A taut string at both ends vibrates in its nth overtone. The distance between adjacent Node and Antinode
is found to be 'd'. If the length of the string is L, then
(A) L = 2d (n + 1) (B) L = d (n + 1) (C) L = 2dn (D) L = 2d (n – 1)
Q.16 A metallic wire of length L is fixed between two rigid supports. If the wire is cooled through a temperature
difference T (Y = young’s modulus,  = density,  = coefficient of linear expansion) then the frequency
of transverse vibration is proportional to :
 Y  
(A) Y (B) (C) (D)
 Y Y
 20 
Q.17 A standing wave y = A sin   x cos (1000t) is maintained in a taut string where y and x are
3
expressed in meters. The distance between the successive points oscillating with the amplitude A/2
across a node is equal to
(A) 2.5cm (B) 25cm (C) 5cm (D) 10cm