Physics Test

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Physics Test - 1

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Question 1
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Directions: The following question has four choices, out of which one or more can be correct.
The coordinates of a particle moving in a plane are given by:
x(t) = a cos (pt) and y(t) = b sin (pt), where a, b (< a) and p are positive constants of appropriate dimensions.
Which of the following statements is/are correct ?

A
The path of the particle is an ellipse.

B
The velocity and acceleration of the particle are normal to each other at (t = π/2p)

C
The acceleration of the particle is always directed towards a focus.

D
The distance travelled by the particle in time interval t = 0 to t = π/2p is a.

Solution

\(x=a \cos (p t), y=b \sin (p t)\)
Equation of path in \(x\) -y plane is \(\left[\frac{x}{a}\right]^{2}+\left[\frac{y}{b}\right]^{2}=1\)
i.e., the path of the particle is an ellipse. Position vector of a point \(P\) is \(\vec{r}=a \cos p t \hat{i}+b \sin p t \hat{j}\)
\(\Rightarrow \vec{v}=p(-a \sin p t \hat{i}+b \cos p t \hat{j})\)
and \(\vec{a}=-p^{2}(-a \cos p t \hat{i}+b \sin p t \hat{j})=-p^{2} \vec{r}\)
Acceleration of directed towards the centre. Also, \(\vec{v} \cdot \vec{a}=0 at t=\pi / 2 p\)
At \(t=0, \vec{r}=a \hat{i}\)
At \(t=\pi / 2 p, \vec{r}=b \hat{j}\)
So in time \(t=0 \rightarrow t=\pi / 2 p,\) particle goes from A to \(\mathrm{P}\) travelling a distance more than a.

Hence, the correct options are (A), (B) and (C).
Question 2
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Directions: Mark the correct statements.

A
Line spectra contains information about atoms only.

B
Line spectra contains information about both atoms and molecules.

C
Band spectra contains information about both atoms and molecules.

D
Band spectra contains information about molecules only.

Solution

Line mission spectra can be obtained for both atoms and molecules, an atom or molecule in an excited state emits photons by making transition from excited state to ground state. Thus, constituting line emission spectra.
The wavelength emitted by molecular energy levels, which are generally grouped into several bunches, are also grouped and each group is well separated from each other.
The spectrum in this case looks like a band spectrum.
Question 3
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Directions: The following question has four choices, out of which ONE or MORE can be correct.
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 the 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,

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

B
the kinetic energy of the A-B system, at maximum compression of the spring, is mv²/4

C
he maximum compression of the spring is v √(m/k)

D
the maximum compression of the spring is v √(m/2k)

Solution
Question 4
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In YDSE, the source S is not symmetrically placed from the slits S1 and S2 (in figure).

If the separation between slits and screen is D (d < < D), then

A
the central fringe shifts by (√2 - 2)D above the previous location of central fringe

B
the shift in the third bright band of red colour is more than that of yellow colour

C
all the fringes have same shift and no change in brightness

D
the pattern becomes unsymmetrical about the original central fringe

Solution
Question 5
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Directions: The following question has four choices, out of which ONE or MORE can be correct.
A simple pendulum of length L and mass (bob) M is oscillating in a plane about a vertical line between angular limits -Φ and +Φ. For an angular displacement (θ|θ| <Φ ), the tension in the string and the velocity of the bob are T and v, respectively. The relation(s) that hold(s) good under the above conditions is/are:

A
T cos θ = Mg

B
T - Mg cosθ = Mv²/L

C
The magnitude of the tangential acceleration of the bob |aT| = g sinθ

D
T = Mg cos θ

Solution
Question 6
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Consider a flat car of mass m0 on a smooth horizontal plane, that starts moving to right under action of constant horizontal force F, which starts acting at t = 0. At the same instant, sand starts spilling on the flat car from moving hopper as shown in the given figure. The velocity of hopper is constant and is equal to v0 and is acting in direction apposite to F. The velocity of loading is constant and is equal to μ kg/s. Which of the following statements based on the above information is/are correct?

A
Initial acceleration of flat car is equal to F/m_o

B

C
Kinetic energy of the loaded car, at any instant, is less than work done by force F up to this instant.

D
Momentum of loaded car, at any instant, is equal to impulse of force F up to this instant.

Solution

As the sand particles come into contact with the car, they start moving with car's velocity i.e. the collision between sand particles and car is inelastic and some loss of energy takes place. As there is no external force in horizontal direction acting on system, so momentum of the loaded car = Impulse of F
Question 7
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A stepped cylinder, with thread wound around smaller diametre, is released from rest and the cylinder moves down. Then,

A
frictional force, if any, acts up the include

B
coefficient of friction should be more than tan θ

C
coefficient of friction should be less than tan θ/2

D
the cylinder cannot roll without slipping

Solution
Question 8
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For Fresnel type of diffraction, the wave front required is:

A
Plane

B
Cylindrical

C
Triangular

D
Square
Solution
Diffraction of light is the phenomenon of bending of light from the sharp corners of a slit or obstacle and spreading into the region of the geometrical shadow. Diffraction can occur only when the wavelength of light is comparable to the size of the obstacle or the width of the slit.
Diffraction is of two types:
1. Fresnel Diffraction- is the type of diffraction which occurs when the light source lies at a finite distance from the slit.
2. Fraunhofer Diffraction- is the type of diffraction which occurs when a plane wavefront is incident on the slit and the wavefront emerging from the slit is also plane.
So, for Fresnel type of diffraction, the wavefront required is Cylindrical.
Question 9
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The first law of thermodynamics represents conservation of:

A
Heat

B
Work

C
Momentum

D
Energy
Solution
The first law of thermodynamics is a restatement of the law of conservation of energy. It states that energy cannot be created or destroyed in an isolated system; energy can only be transferred or changed from one form to another. When heat energy is supplied to a thermodynamic system or any machine: Two things may occur:
- The internal energy of the system or machine may change.
- The system may do some external work.
Question 10
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Comets move around the sun in highly elliptical orbits. The gravitational force on the comet due to the sun is not normal to the comet’s velocity in general. Yet the work done by the gravitational force over every orbit of the comet is zero. Why?

A
The gravitational force is conservative, hence work done is zero.

B
The gravitational force is non-conservative, hence work done is zero.

C
Energy is absent, hence work done is zero.

D
Force is in negative direction.

Solution

The gravitational force acting on the comet is a conservative force. The work done by a conservative force is equal to the negative of the change in potential energy. Over a complete orbit of any shape, there is no change in the potential energy of the comet. So, no work is done by the gravitational force on the comet.