### Numerical Problem

52. A force of 5N acts on a body of weight 10N the acceleration of body is **[2075]**

50 m/s^{2}

2 m/s^{2}

5 m/s^{2}

0.5 m/s^{2}

Weight = Mass * Gravity

10 = M * 9.8

Mass = 1 kg

5 = 1 * a

a = 5 m /s

^{2}

56.A rain drop of radius 0.3mm has terminal velocity 1m/s in air.The viscosity of air is 18 x 10^{-5} poise, then viscous force is **[2075]**

1.01 x 10^{-7}N

1.01 x 10^{-8}N

1.6 x 10^{-9}N

1.6 x 10 ^{-8}

Terminal velocity $v_{c}$ =1m/s = 100 cm/s

Viscosity of air η=18×10

^{−3}poise

Viscous force $ F=6πηrv_{c}$

∴ F=6π×18×10

^{−3}×0.03×100=1.0178 dyne

58.A glass vessel contains air at 27°C the temperature to which it must be
heated so that one-fourth of air is expelled from it at constant pressure is **[2075]**

47°C

77°C

102°C

127°C

At temperature T , the no. of moles left = n - 1/4 - 3n/4

At constant pressure and volume, n

_{1}T

_{2}=n

_{2}T

_{2}

n x 300 = 3n/4 x T

300n = 3n

1200 = 3 x T

400 = 3T

127

60. A cylinder of 0.6 m long and 6mm radius is rated at 1.5 kW.the temperature of filament if Stefan’s constant is 6 x 10^{-8} Wm ^{-2}K ^{-4} **[2075]**

920K

1125K

1025K

1320K

61. Light of wavelength 550 nm falls normally on a slit of width 22 x 10^{-7}m, the angular position of second minima from central maxima will be **[2075]**

14.5°

30°

42°

62°

Here, n = 2

$sinθ = {2 × 550 × 10^{-9} \over {22 x 10^{-7}}}$

$sinθ = {1\over2} $

$θ = π \over 6$

$θ = 30°$

62. Two lens of power 5D and -7.5D are placed in contact.The equivalent focal length of combination will be **[2075]**

-40cm

+40cm

-25cm

+25cm

${ 1 \over f } = {1\over{f_1}} + {1\over{f_2}} $

${ 1 \over f } = 5 - 7.5 $

$ { 1 \over f } = 2.5 $

f = { 1 \over 2.5 m}

-25cm

63. The length of the microscope is 14 cm and magnifying power is 25 for relaxed eye the focal length of the eyepiece is 5 cm then a distance of object from
objective is **[2075]**

2.4cm

2.1cm

1.5cm

1.8cm

$⇒14=v_{o}+5$

$⇒v_{o}=9cm $

Magnifying power of microscope for relaxed eye

$m = {v_o \over u_o}.{D\over f_{e}}$

$25 = {9 \over u_o}.{25\over 5}$

$u_o = {9 \over 5}$

1.8cm

64. A sound wave has frequency 500Hz and velocity 360m/s. What is the
distance between 2 particles having phase difference 60° **[2075]**

0.7cm

1.2cm

70cm

12cm

velocity (v)=360m/s

∴ wavelength = velocity/frequency

λ = 360m/s / 500 = 0.72m

60° out of phase implies that the wavelength between two points is

${x\over60°} = {0.72m \over 360°}$

x = 0.12m

or 12cm

67.A wire of resistance 12Ω is bent to form a circle.The effective resistance
between the two points on any diameter of circle is **[2075]**

12Ω

9Ω

6Ω

3Ω

69. A 10 eV electron is circulating in a plane at right angles to a uniform field
of magnetic induction 10^{-4}, the orbital radius of the electron is **[2075]**

18cm

16cm

11cm

9cm

K=10eV

B=10

^{−4}Wb/m

^{2}

Using : mv=Bqr where mv=√2Km

$r = \sqrt{2Km\over B^2q^2}$

$r = \sqrt{2 × 9.1 × 10^{-31} × 10e \over {(10^{-8})e^2}}$

$r = \sqrt{2 × 9.1 × 10^{-31} × 10e \over {(10^{-8})e^2}}$

$1.06 × 10^{-2}m$

11cm

74. A nucleus reactor has a power of 16 kW if the energy per fission is 200
MeV then number of fissions per second is **[2075]**

5 x 10^{17}

5 x 10^{16}

5 x 10^{15}

5 x 10^{14}

Energy per fission =200MeV

$ P = n({E\over{t}})$

$ 16 × 10^3 ={ n × 200 × 10^6 × 1.6 ×10^{-19} \over t} $

$ {n\over{t}} = 5 × 10^{14} $

(Given 1eV=1.6×10

^{−19}J )

56. If a 200m bridge of steel has length from, temperature varies from 243K us 313K, The change of length of bridge for above seasonal variation in temperature (α_{steel} = 11 × 10^{-6}) **[2074]**

15.4 cm

15.9 cm

15.8 cm

10 cm

_{i}= 200m

The initial temperature is: T

_{t}= 243k

The final temperature is: T

_{f}=313k

The coefficient of linear expansion of steel is: (α

_{steel}= 11 × 10

^{-6})

ΔL

_{o}=L

_{i}α

_{s}(T

_{f}−T

_{i})

ΔL

_{o}=200×11×10

_{−5}(313−243)

=1.54m or 15.4cm

61. While standing still, an observer measures frequency of tuning fork to be 524 Hz. What frequency does he measure as he approaches the form at Sm/s ? (speed of sound in air = 340 m/s)**[2074]**

500 Hz

420 Hz

520 Hz

532 Hz

65. If critical angle for a material placed in air is 30° the refractive index will be **[2074]**

2

0.5

1.5

2.5

$θ_c=sin^{−1}({{n_2}\over{n_1}})$

${{n_2}\over{n_1}}=sin(θ_c)$

${{n_2}\over{n_1}}= 0.5$

since Second medium is air n2 = 1

n1 = n2/0.5

n1 = 2

66. A body has 1c of negative charge. How many excess electron it has as compared to its neutral state? **[2074]****[2074]**

6.25 x 10^{18}

6.25 x 10^{-19}

1.6 x 10^{-19}

1.6 x 10^{18}

1 = n x 1.6 x 10

^{-19}

n = 1/1.6 x 10

^{-19}

n = 10

^{19}/1.6

n = ${100\over16}×10^{18}$

n = 6.25 x 10

^{18}

71. The self inductance of coil is MH. If a current of 2a is flown. What is the magnetic flux through coil? **[2074]**

0.02 Wb

0.01 Wb

0.05 Wb

10 Wb

53. A man walks 8 m forwards East and 6m towards North. The magnitude of displacement is **[2073]**

14m

2m

8m

(8^{2} + 6^{2})m

Using pythagoras theorem P

^{2}= 8

^{2}+ 6

^{2}

54. If initial velocity of a projectile is doubled, the maximum range will by **[2073]**

2 times

4 times

8 times

16 times

Since angle and G is constant

$ R ∝ u^2 $

${R' \over R} = {(u')^2 \over u^2} $

$R' = {(2u)^2 \over u^2} R $

$R = 4R$

57. A weightless rubber balloon has 100g of water in it. Its weight in water will be **[2073]**

100g

50g

> 100g

zero

58. The temperature of a substance increase by 270°C. This increase is equal to **[2073]**

300k

0k

27k

273k

63. A person cannot see objects clearly beyond 50 cm. The power of the lens to correct the vision is **[2073]**

+5D

-5 D

-0.5 D

-2 D

$P = 100 \over -50$

$P = -2 D$

65. Three capacitors each of capacitance 3pF are connected in series. The net capacitance is **[2073]**

1μF

(1/3)μF

3μF

9μF

$ {1\over c' }= {1\over 3} + {1 \over 3} + {1\over 3}$

$3\over 3 = 1$

72. The equation of sound wave is y = 0.0015 sin(62.4x + 316t) the wave length of sound wave is **[2073]**

0.2 unit

0.1 unit

3.3 unit

not known from the given equation

62.4=2π/wave length

62.4=2×3.14/wave length

Wave length=6.24/62.4

=1/10 =0.1m

73. A wave is reflected from a rigid support. The change of phase on reflection will be **[2073]**

0

π / 2

π / 4

π

51. A force F = $\overrightarrow{\mathrm{2i}}+\overrightarrow{\mathrm{3j}}-\overrightarrow{\mathrm{4k}}$ newton acts on a body. In 5 seconds the force displaces the body through a displacement S = $\overrightarrow{\mathrm{3i}}+\overrightarrow{j}-\overrightarrow{\mathrm{2k}}$ meter. The power (in watt) of the force is **[2072]**

4.3

3.4

5.4

6.3

52. Two simple harmonic waves are represented respectively by y1 = A1 sin ωt and y2 = A2 cos ωt. The phase difference between the two wave is**[2072]**

3π / 2

π

π/2

π/4

53. A river is flowing west to east at a speed of 5 m/min. A man on the south bank of the river, capable of swimming at 10m/min in still water, wants to swim across the river by the shortest path. He should swim in the direction**[2072]**

due north

30° East of North

60° East of North

30° West of North

57. At what temperature the rms velocity of a hydrogen molecule be equal to that of oxygen at 47°C **[2072]**

-273°C

273K

20K

20°C

59. A square plate of side 2 units is heated through 10°C. If the linear exansivity of the material is x, increase in the surface area of the plate is **[2072]**

480x

80x

240x

240x^{2}

60. A black body radiates heat energy at the rate of 2 x 10 ^{5}Js''m' at a temperature of 127°C. The temperature of the black body at which the rate of heat radiation is 32 x 10^{5} is **[2072]**

327°

927°

527°

727°

64. Two vehicles are approaching each other with a speed of 10ms^{-1}. If A emits a note of 1000 vibrations, what will be the frequency of the note of 1000 vibration, what will be the frequency of the note as heard by a person sitting in B if the velocity of sound is 330 ms^{-1}? **[2072]**

950Hz

1000 Hz

1062.5 Hz

1215.5 Hz

65. An open pipe and a closed pipe resonate to the same tuning fork. The ratio of their lengths is **[2072]**

1:1

2:1

1:2

4:1

67. A 25W, 120V lamp and 100W, 120V lamp are connected in series across a 120V line. Which lamp will burn more brightly **[2072]**

25W, 120V

100W, 120V

Both will have same brightness

Alternatively both may be bright, one at a time.

69. The ratio of induced emf in a coil having 50 turns and rotating with 50
Hz to that of induced emf in a coil having 100 turns and rotating with
150 Hz in the same magnetic field is **[2072]**

1:2

2:3

1:6

3:2

70. A 0 - 100mA resistance 1ft is to be converted to an ammeter in the range of 0-1A. We have to use shunt **[2072]**

1Ω

0.1Ω

0.111Ω

0.055Ω

71. The ratio of specific charge of proton to that of an alpha particle is **[2072]**

1:4

1:2

4:1

2:1

Therefore specific charge of alpha particle = 2p ( ∵α particle has 2 protons and 2 neutrons,

Therefore, ratio of specific charge of protons to alpha particles = 2p/p = 2/1 ⇒1:2

74. The kinetic energy of a particle is doubled, de Broglie wavelength becomes **[2072]**

2 times

4 times

2 times

1/√2 times

$λ ={ h \over \sqrt{2mE}}$

If kinetic energy is double then λ = $1\over \sqrt{ 2}$

56. The depth of water at which air bubble of radius 0.4mm may remain in equilibrium (surface tension of water = 72 x 10^{-3} N/m, g = 9.8 m/s^{2} is given by **[2071]**

7.348 cm

0.918 cm

3.674 cm

1.837 cm

^{−3}N/m

R = 0.4×10

^{ −3}m

P

_{water}= 10

^{3}kg/m

^{3}

g = 9.8m/s

^{2}

Now,

$ hdg = {2T \over R}$

$ h = {2T \over{ pgR}} = {2 × 72 ×^{-3} \over {10^3 × 9.8 × 0.4 × 10^{-3} }}$

57. When a cylinder is heated, it's length increases by 2%, the area of its base will increase by: **[2071]**

0.5%

1%

2%

4%

60. The efficiency of Carnot engine working between steam point and ice point is: **[2071]**

16.8%

26.8%

36.8%

46.8%

Temperature of sink, T2= 0˚C= 273 K

$ η = 1 - {T_c \over T_h} $

$ 1 - { 273 \over 373} = 0.268 $ 26.8

69. The radius of Earth 6400 km. The capacitance is **[2071]**

6400 MF

6400 F

1 F

711 μF

^{3}m

ε_o = 8.85 x 10

^{-12}

$ C = 4πε_oR_1$

C = 4 × 3.14 × 8.85 ×. 10

^{--12}× 6400 × 10

^{-4}

C = 7.11 x 10

^{-6}F

C = 711 μF

70. Two wire of same material have lengths L and 2L and are cross reaction areas 4A and A respectively. The ratio of their specific resistance would be **[2071]**

1:1

1:8

8:1

1:2

$ R_1 \over R_2$ = ${pl_1 \over A_1} \over {pl_2 \over A_2}$

Here p is resistivity of material so it will be same

$ R_1 \over R_2$ = $l_1 \over A_1$ x $A_2 \over l_2$ $ R_1 \over R_2$ = $l \over 4A$ x $A \over 2l$

1:8

74. The half-life of a substance is 1600 years. The mean life is **[2071]**

1600 yrs

3200 yrs

800 yrs

2309 yrs

55. Two wires A and B are of the same material. Their lengths are in the ratio of 1:2 and diameters are in the ratio of 2:1. If they are pulled by the same force, their increase in length will be in the ratio. **[2070]**

2:1

1:4

1:8

8:1

Since Y, F are same for both the wires, we have,

$1\over {r_1}^2$ $L_1 \over l_1$ = $1 \over {{r_2}^2} $$L_2 \over l_2$

$l_1 \over {l_2} $ = $ {r_2}^2 × L_1 \over {r_1}^2 × L_2$

$l_1 \over {l_2} $ = $ {D_2 \over 2}^2 × L_1 \over {D_1 \over 2}^2× L_2$

$l_1 \over {l_2} $ = $ {D_2}^2 × L_1 \over {D_1 }^2× L_2$

$l_1 \over {l_2} $ = $ {D_2}^2 \over {2D_2 }^2$ x $L_2 \over 2L_2$ = $1\over 8$

$l_1 : l_2 = 1:8$

56. Water is flowing through a tube of the non-uniform cross-section. If the radius of the tube at the entrance and the exit is 3:2, then the ratio of the velocity of liquid entering and leaving the tube is:

8:27

4:9

9:4

1:1

$π(3)^2.V_1 = π(2)^2.V_2$

${V_1 \over V_2 }= {4 \over 9}$

58. 50g of ice at -6°C is dropped into the water at 0°C. how many grams of water freeze? Sp. Heat capacity of ice=2000JKg^{-1}C^{-1}.**[2070]**

1.785 g

4.25 g

3.16 g

9.33 g

60. The temperature of source and sink of carnot engine are 400k and 300k respectively. What is it's efficiency?**[2070]**

100%

75%

33.33%

25%

These are the temperatures of source and sink respectively

The efficiency of the cycle is,

$η=1−{t\over{T}}$

η=1−0.75=0.25

Thus the efficiency is 25 %

61. The refractive index of air with respect to glass is 2/3. The refractive index of diamond with respect to air is 12/5. Then the refractive index of glass with respect to diamond will be. **[2070]**

5/8

8/9

5/18

18/5

$ μ_{diamond} \over μ_{air} $ = $ 12\over5$

on multiply we get

$ μ_{diamond} \over μ_{glass} $ = $ 8\over5$

$ μ_{glass} \over μ_{diamond} $ = $ 5\over8$

63. Light of wave length 7200 Å in air has wave length in glass equal to ......... (given Refractive index of glass with respect to air = 1.5)**[2070]**

7200 Å

4800 Å

1080 Å

10800 Å

7200 Å / 1.5

4800

64. Three capacitor of capacitance 3µF, 9µF and 18µF are connected first in series and then I parallel. the ratio of C equivalent capacitance in two cases (CI/CP) will be**[2070]**

1:15

15:1

1:1

1:3

$1 \over{C_s}$ = $ 1 \over 2$

${C_s}$ = 2μF

${C_p}$ = 3 + 9 + 18 = 30 μF

${C_s}\over{C_p}$ = $2\over30 $ = $1\over 15$

66. The resistance of two lamp are in ratio of 1:2. Their wattage will be in the ratio of**[2070]**

1:2

2:1

4:1

1:4

67. The energy stored in 50mH inductor carrying a current of 4A is .......**[2070]**

0.1 J

0.4 J

0.3 J

0.01 J

I = 4A

$ E = {1\over 2 }LI^2$

E = 0.4 J

69. A particle of mass 10^{-31} kg is moving with a speed of 10^{5}m/s. The De-Broglie wavelength of the particle is ...... **[2070]**

6.63 x 10^{-8} m

6.63 Å

66.3 Å

6.63 x 10^{-7}m

$ λ = {6.63 × 10^{-34} \over {10^{-31} × 10^5}} $

λ = 6.63 x 10

^{-8}m

73. A common emitter transistor amplifier has a current fain of 50. If the load resistance is 4 kΩ and the input resistance is 500 Ω. The voltage gain on the amplifier is ....... **[2070]**

400

6.2

500

300

R

_{L}=4kΩ

R

_{i}=500Ω

The resistance gain is given by,

$R_L \over R_{i} $ = $4000 \over 500$ = 8

Now, the voltage gain is

$A_v = β $($R_L \over R_{i} $)

$A_v$ = 50 x 8 = 400

74. A tube closed at one end has a resonating length 1 meter. The air column in the pipe can resonate for sound of frequency ..... (V = 320ms^{-1})**[2070]**

166 Hz

249 Hz

575 Hz

80 Hz

75. A displacement wave is represented by y = 0.025 sin(5006 - 0.0025x), where y,t and x are in cm, second and meter respectively. The wave length of wave is .......**[2070]**

20π m

40 π m

60 π m

80 π m