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1 Wave Optics

Unpolarised light converts to partially or plane polarised light by many processes. which of the following does not do that?

(1) Double refraction

(2) Scattering

(3) Reflection

(4) Diffraction.

2 Ray Optics

The magnification of an object placed in front of a convex lens of focal length 20 cm is is +2. To obtain a magnification of -2, The object has to be moved a distance equal to:

1) 10 cm

2) 20 cm

3) 30 cm

4) 40 cm

It is given that a convex lens of focal length

$$ f=+20\,cm $$

$$ m=+2 $$

$$ \because m=\dfrac{v}{u} $$

$$ v=2u..........(1) $$

Using lens formula

$$ \dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f} $$

$$ \dfrac{1}{2u}-\dfrac{1}{u}=\dfrac{1}{20} $$

$$ u=-10\,cm $$

Hence, object is placed at a distance of 10 cm in front of lens.

3 Gravitation

Satellite is moving around the Earth in a circular orbit with a velocity V. If the gravitational force of the Earth were to suddenly disappear, then the satellite would

1) move with a velocity V, tangentially to its circular orbit.

2) fall towards the surface of the Earth.

3) move radially outwards with a velocity V.

4) spirally move away from the Earth.

The satellite is held in orbit because of two forces. One is the gravitational force and the second is the centrifugal force. When the gravitational force disappears, there is no force to hold it in orbit. So it moves in the direction of its velocity, which is tangential to the circular path it was describing earlier.

4 Laws of Motion

A body of mass M just starts sliding down an inclined plane ( rough) with inclination θ. such that tanθ=1/3. The force acting on body down the plane in this position is

1) Mg

2) Mg/3

3) (2/3)Mg

4) Mg/√10

**Solution**

tanθ=1/3

∴ sinθ=1/√10

Downward force=Mgsinθ

Down ward force=Mg(1/√10)

5 Laws of Motion

A ball of mass 0.2 kg is thrown vertically upwards by applying a force by hand. If the hand moves 0.2 m which applying the force and the ball goes upto 2 m height further, find the magnitude of the force. Consider g = 10 m/s^{2}

1) 22 N

2) 4 N

3) 16 N

4) 20 N

**Solution**

Work done by hand = Potential energy of the ball

6 Dual Nature of Matter and Radiation

The number of photo electrons emitted for light of a frequency v (higher than the threshold frequency v0) is proportional to :

1) Frequency of light (v)

2) $$v-v_0$$

3) $$Threshold\;frequency\;(v_0)$$

4) Intensity of light

7 Oscillations

A pendulum having a period of oscillation of 2 seconds is taken on a planet where g is four times that on the earth. The period of the pendulum would be

1) 4 s

2) 2 s

3) 1 s

4) ½ s

SOLUTION

8 Waves

A transverse wave propagating on the string can be described by the equation y=2sin(10x+300t).. where x and y are in metres and tt in second. If the vibrating string has linear density of 0.6×10^{−3}g/cm then the tension in the string is

1) 5.4N

2) 0.054N

3) 54N

4) 0.0054N

General equation of progressive wave:

y=Asin(ωt+kx)

Here, A is amplitude

ω is angular frequency

k is propagation constant

t is time

x is displacement

Given equation:

y=2sin(10x+300t)..

Linear charge density, μ=0.6×10^{−3}g/cm=6×10−3kgm^{−1}

Compare with general equation:

Velocity of the wave in the string:

v=ω/ k = 300 / 10 = 30ms^{−1}

Relation for velocity in terms of tension:

T=μv^{2} = 6×10^{−3 }× (30)^{2 }= 5.4N

Hence, tension in string is 5.4N

9 Gravitation

The radius of the Earth is 4 times that of the moon and its mass is 80 times that of the moon. If the acceleration due to gravity on the surface of the earth is 10 m/s^{2}, then the acceleration on the surface of the moon will be:

1) 0.98 m/s^{2}

2) 1.47 m/s^{2}

3) 1.96 m/s^{2}

4) 0.49 m/s^{2}

Solution

Acceleration due to gravity

$$\displaystyle{g}=\frac{{{G}{M}}}{{{R}^{{{2}}}}}$$

$$\displaystyle\therefore\frac{{{g}_{{{m}{o}{o}{n}}}}}{{{g}_{{{e}{a}{r}{t}{h}}}}}=\frac{{{M}_{{{m}{o}{o}{n}}}}}{{{M}_{{{e}{a}{r}{t}{h}}}}}.\frac{{{{R}_{{{e}{a}{r}{t}{h}}}^{{{2}}}}}}{{{{R}_{{{m}{o}{o}{n}}}^{{{2}}}}}}={\left(\frac{1}{{80}}\right)}{\left(\frac{4}{{1}}\right)}^{{{2}}}$$

$$\displaystyle{{g}_{{{m}{o}{o}{n}}}=}{{g}_{{{e}{a}{r}{t}{h}}}\times}\frac{16}{{80}}=\frac{g}{{5}}$$

10 Physical world and measurement

An isolated** **conductor will become polarized (in terms of charge) when:

(1) it is touched by a charged object.

(2) it is warmed.

(3) it is brought close to (but not touching) a charged object.

(4) it is charged with a power supply

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