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1 Magnetic Effects of Current and Magnetism

At the mid-point along the length of a long solenoid, the magnetic field is equal to x, If the length of the solenoid is doubled and the current is reduced to half, the field at the new mid-point will be nearest to:

(1) x/2

(2) x/4

(3) x

(4) 2x

**Solution**

x/4

2 Properties of Bulk Matter

A wind with speed 40 m/s blows parallel to the roof of a house. The area of the roof is 250 m^{2}. Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be: ( ρair=1.2 kg/m^{3})

1) 4.8×10^{5}N, upwards

2) 2.4×10^{5}N upwards

3) 4.8×10^{5}N downwards

4) None of these

Let p1 and p2 are pressure inside and outside the roof and v1 and v2 are velocities of the wind inside and outside the roof.

According to Bernoulli’s theorem

3 Oscillations

A source of sound S emitting waves of frequency 100 Hz and an observer O are located at some distance from each other. The source is Find the time period of oscillations of a torsional pendulum, if the torsional constant of the wire is K = 10π^{2}J/rad. The moment of inertia of rigid body is 10 Kg m^{2} about the axis of rotation.

1) 2 sec

2) 4 sec

3) 16 sec

4) 8 sec

Time period of a torsional pendulum is given by

4

The number of photons emitted per second by a 25 W source of monochromatic light of wavelength 6000 A° is:

1. 6.23 X 10^{19}

2. 6.86 X 10^{17}

3.7.54 X 10^{19}

4. 7.23 X 10^{18}

5 Ray Optics

The image formed in a plane mirror is

(1) real and the same size as the object

(2) real and nearly the same size as the object

(3) virtual and the same size as the object

(4) virtual and the half the size of the object

6 Capacitance

Combination of two identical capacitors, a resistor R and a dc voltage source of voltage 6V is used in an experiment on a (C-R) circuit. It is found that for a parallel combination of the capacitor the time in which the voltage of the fully charged combination reduces to half its original voltage is 10 second. For series combination the time needed for reducing the voltage of the fully charged series combination by half is?

1) 2.5 second

2) 20 second

3) 10 second

4) 5 second

q = q_{0}e^{t/τ }

⇒q=q_{0}/2⇒=t=Γln2

t = R(2C)ln2 for first case

t = R(C / 2)ln2 for second case

∴ t = 2.5 sec.

7 Electronic Devices

Work function for a surface is equal to :

(1) Φ = fermi energy – binding energy

(2) Φ =fremi energy

(3) Φ = binding energy – fermi energy

(4) Φ = binding energy

8 Wave Optics

In a double slit experiment, the two slits are 1 mm apart and the screen is place 1 m away. A monochromatic light of wavelength 500 nm is used. What will be the width of each slit for obtaining ten maxima of double slit within the central maxima of single slit pattern?

1) 0.5mm

2) 0.02mm

3) 0.2mm

4) 0.1mm

$$d = 10^{-3}\:m$$

$$D=1\:m$$

$$ \lambda = 500 \times 10^{-9}\:m$$

The width of central maxima in a single slit diffraction: $$\dfrac{2 \lambda D}{a}$$

Fringe width in double slit pattern: $$\beta = \dfrac{\lambda D}{d}$$

Given,

$$10 \beta = \dfrac{2 \lambda D}{a}$$

$$ \Rightarrow 10 \dfrac{\lambda D}{d} = \dfrac{2 \lambda D}{a}$$

$$ \Rightarrow a =\dfrac{d}{5}\:mm= 0.2\:mm$$

9 Magnetic Effects of Current and Magnetism

A conducting loop lies in the plane of this page and carries a clockwise induced current. Which of the following statements could be true?

(1) A constant external magnetic field is directed into the page.

(2) A constant external magnetic field is directed out of the page.

(3) An increasing external magnetic field is directed into the page.

(4) A decreasing external magnetic field is directed into the page.

10 Ray Optics

A beam of monochromatic ligh first travels through glass of R.I. 1.5 and then through water (R.I. =4/3). If the difference in their wavelength in the two media is 40nm, then the wavelength of the monochromatic light in vacuum will be

1) 4000 Å

2) 4400 Å

3) 4800 Å

4) 5200 Å

$$\displaystyle{5200}Å$$

$$\displaystyle\therefore\lambda_{{w}}-\lambda_{{g}}=\lambda_{{a}}{\left[\frac{{{3}}}{{{4}}}-\frac{{{2}}}{{{3}}}\right]}=\frac{{\lambda_{{a}}}}{{{12}}}={40}\times{10}^{{-{9}}}$$

∴λa=12×40×10^{−9 }= 4800Å

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