Graphical Questions

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Questions 1 of 25

Question:Two blocks of masses 10 kg and 4 kg and are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of 14 m/s to the heavier block in the direction of the lighter block. The velocity of the centre of mass is

Answers Choices:

30 m/s

20 m/s

10 m/s

5m/s

Questions 2 of 25

Question:Two particles of masses \({m_1}\) and \({m_2}\) in projectile motion have velocities \({\vec v_1}\) and \({\vec v_2}\) respectively at time t = 0. They collide at time t0. Their velocities become \({\vec v_1}\) and \({\vec v_2}\) at time 2\({t_0}\) while still moving in air. The value of (\({m_1}\)\({\vec v_1}\)+ \({m_2}\)\({\vec v_2}\)) - (\({m_1}\)\({\vec v_1}\) + \({m_2}\)\({\vec v_2}\)) | is

Answers Choices:

zero

\(({m_1} + {m_2})g{t_0}\)

\(2({m_1} + {m_2})g{t_0}\)

\(\frac{1}{2}({m_1} + {m_2})g{t_0}\)

Questions 3 of 25

Question:An isolated particle of mass m is moving in horizontal plane (x-y), along the x-axis, at a certain height above the ground. It suddenly explodes into two fragment of masses m/4 and 3m/4. An instant later, the smaller fragment is at y =+15 cm. The larger fragments at this instant is at

Answers Choices:

y = - 5 cm

y = +20 cm

y = +5 cm

y = -20 cm

Questions 4 of 25

Question:A shell is fired from a cannon with a velocity v at an angle 9 with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon and the speed of the other piece immediately after the explosion is:

Answers Choices:

3vcos\(\theta \)

2vcos\(\theta \)

3/2 vcos\(\theta \)

\(\sqrt {3/2} \) v cos\(\theta \)

Questions 5 of 25

Question:Two blocks A and B each of mass m are connected by a massless spring of natural length L and spring constant K. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length, as shown in figure. A third identical block C, also of mass m, moves on the floor with a speed v along the line joining A and B, and collides elastically with A. Then

Answers Choices:

The kinetic energy of the A-B system at maximum compression of the spring, is zero

The kinetic energy of the A-B system, at maximum compression of the spring, is \(m{v^2}/4\)

The maximum compression of the spring is \(v\sqrt {(m/K)} \)

The maximum compression of the spring is \(v\sqrt {(m/2K)} \)

Questions 6 of 25

Question:A ball hits the floor and rebounds after an inelastic collision. In this case,

Answers Choices:

the momentum of the ball just after the collision is the same as that just before the collision.

the mechanical energy of the ball remains the same in the collision.

the total momentum of the ball and the earth is conserved.

the total energy of the ball and the earth is conserved

Questions 7 of 25

Question:A ray of light of intensity I is incident on a parallel glass-slab at a point A as shown in fig. It undergoes partial reflection and refraction. At each reflection 25% of incident energy is reflected. The rays AB and A'B' undergo interference. The ratio \({I_{\max }}/{I_{\min }}\) is

Answers Choices:

4:1

8:1

7:1

49:1

Questions 8 of 25

Question:A thin slice is cut out of a glass cylinder along a plane parallel to its axis. The slice is placed on a flat glass plate as shown. The observed interference fringes from this combination shall be

Answers Choices:

Straight

Circular

Equally spaced

Having fringe spacing which increases as we go outwards

Questions 9 of 25

Question:In the figure is shown Young's double slit experiment. Q is the position of the first bright fringe on the right side of O. P is the 11th fringe on the other side, as measured from Q. If the wavelength of the light used is \(6000 \times {10^{ - 10}}m\), then \({S_1}B\) will be equal to

Answers Choices:

\(6 \times {10^{ - 6}}m\)

\(6.6 \times {10^{ - 6}}m\)

\(3.138 \times {10^{ - 7}}m\)

\(3.144 \times {10^{ - 7}}m\)

Questions 10 of 25

Question:A monochromatic beam of light falls on YDSE apparatus at some angle (say \(\theta \)) as shown in figure. A thin sheet of glass is inserted in front of the lower slit \({S_{\rm{2}}}\). The central bright fringe (path difference = 0) will be obtained

Answers Choices:

At O

Above O

Below O

Anywhere depending on angle \(\theta \), thickness of plate t and refractive index of glass \(\mu \)

Questions 11 of 25

Question:Two ideal slits \({S_{\rm{1}}}\) and \({S_{\rm{2}}}\) are at a distance d apart, and illuminated by light of wavelength l passing through an ideal source slit S placed on the line through \({S_2}\) as shown. The distance between the planes of slits and the source slit is D. A screen is held at a distance D from the plane of the slits. The minimum value of d for which there is darkness at O is

Answers Choices:

\(\sqrt {\frac{{3\lambda D}}{2}} \)

\(\sqrt {\lambda D} \)

\(\sqrt {\frac{{\lambda D}}{2}} \)

\(\sqrt {3\lambda D} \)

Questions 12 of 25

Question:Two point sources X and Y emit waves of same frequency and speed but Y lags in phase behind X by 2 \(\pi \)l radian. If there is a maximum in direction D the distance XO using n as an integer is given by

Answers Choices:

\(\frac{\lambda }{2}(n - l)\)

\(\lambda (n + l)\)

\(\frac{\lambda }{2}(n + l)\)

\(\lambda (n - l)\)

Questions 13 of 25

Question:A beam with wavelength \(\lambda \) falls on a stack of partially reflecting planes with separation d. The angle \(\theta \) that the beam should make with the planes so that the beams reflected from successive planes may interfere constructively is (where n =1, 2, .........)

Answers Choices:

\({\sin ^{ - 1}}\left( {\frac{{n\lambda }}{d}} \right)\)

\({\tan ^{ - 1}}\left( {\frac{{n\lambda }}{d}} \right)\)

\({\sin ^{ - 1}}\left( {\frac{{n\lambda }}{{2d}}} \right)\)

\({\cos ^{ - 1}}\left( {\frac{{n\lambda }}{{2d}}} \right)\)

Questions 14 of 25

Question:Two coherent sources separated by distance d are radiating in phase having wavelength \(\lambda \). A detector moves in a big circle around the two sources in the plane of the two sources. The angular position of n = 4 interference maxima is given as

Answers Choices:

\({\sin ^{ - 1}}\frac{{n\lambda }}{d}\)

\({\cos ^{ - 1}}\frac{{4\lambda }}{d}\)

\({\tan ^{ - 1}}\frac{d}{{4\lambda }}\)

\({\cos ^{ - 1}}\frac{\lambda }{{4d}}\)

Questions 15 of 25

Question:The diagram shows a force-extension graph for a rubber band. Consider the following statements
i. It will be easier to compress this rubber than expand it
ii. Rubber does not return to its original length after it is stretched
iii. The rubber band will get heated if it is stretched and released
Which of these can be deduced from the graph

Answers Choices:

III only

II and III

I and III

I only

Questions 16 of 25

Question:The stress versus strain graphs for wires of two materials A and B are as shown in the figure. If \({Y_A}\) and \({Y_B}\) are the Young's modulii of the materials, then

Answers Choices:

\({Y_B} = 2{Y_A}\)

\({Y_A} = {Y_B}\)

\({Y_B} = 3{Y_A}\)

\({Y_A} = 3{Y_B}\)

Questions 17 of 25

Question:The load versus elongation graph for four wires of the same material is shown in the figure. The thickest wire is represented by the line

Answers Choices:

OD

OC

OB

OA

Questions 18 of 25

Question:The adjacent graph shows the extension \((\Delta l)\) of a wire of length 1m suspended from the top of a roof at one end with a load W connected to the other end. If the cross sectional area of the wire is \({10^{ - 6}}{m^2},\) calculate the young's modulus of the material of the wire

Answers Choices:

\(2 \times {10^{11\,}}N/{m^2}\)

\(2 \times {10^{ - 11}}N/{m^2}\)

\(3 \times {10^{ - 12}}N/{m^2}\)

\(2 \times {10^{ - 13}}N/{m^2}\)

Questions 19 of 25

Question:The graph is drawn between the applied force F and the strain (x) for a thin uniform wire. The wire behaves as a liquid in the part

Answers Choices:

ab

bc

cd

oa

Questions 20 of 25

Question:The graph shows the behaviour of a length of wire in the region for which the substance obeys Hook's law. P and Q represent

Answers Choices:

P = applied force, Q = extension

P = extension, Q = applied force

P = extension, Q = stored elastic energy

P = stored elastic energy, Q = extension

Questions 21 of 25

Question:The potential energy U between two molecules as a function of the distance X between them has been shown in the figure. The two molecules are

Answers Choices:

Attracted when x lies between A and B and are repelled when X lies between B and C

Attracted when x lies between B and C and are repelled when X lies between A and B

Attracted when they reach B

Repelled when they reach B

Questions 22 of 25

Question:The value of force constant between the applied elastic force F and displacement will be

Answers Choices:

\(\sqrt 3 \)

\(\frac{1}{{\sqrt 3 }}\)

\(\frac{1}{2}\)

\(\frac{{\sqrt 3 }}{2}\)

Questions 23 of 25

Question:The diagram shows stress v/s strain curve for the materials A and B. From the curves we infer that

Answers Choices:

A is brittle but B is ductile

A is ductile and B is brittle

Both A and B are ductile

Both A and B are brittle

Questions 24 of 25

Question:Which one of the following is the Young's modulus (in N/m2) for the wire having the stress-strain curve shown in the figure

Answers Choices:

\(24 \times {10^{11}}\)

\(8.0 \times {10^{11}}\)

\(10 \times {10^{11}}\)

\(2.0 \times {10^{11}}\)

Questions 25 of 25

Question:The diagram shows the change x in the length of a thin uniform wire caused by the application of stress F at two different temperatures T1 and T2. The variations shown suggest that

Answers Choices:

\({T_1} > {T_2}\)

\({T_1} < {T_2}\)

\({T_1} = {T_2}\)

None of these