The correction factor ‘a’ to the ideal gas equation corresponds to
a.
forces of attraction between the gas molecules
Correct Answer
b.
density of the gas molecules
c.
electric field present between the gas molecules
d.
volume of the gas molecules
Step-by-Step AI Explanation
Verified Method
In the van der Waals equation, the 'a' parameter accounts for the intermolecular forces of attraction, while 'b' accounts for the finite volume of the gas molecules.
Q25mcq
Given van der Waals constant for NH3, H2, O2 and CO2 are respectively 4.17, 0.244, 1.36 and 3.59, which one of the following gases is most easily liquefied?
a.
CO2
b.
NH3
Correct Answer
c.
O2
d.
H2
Step-by-Step AI Explanation
Verified Method
The van der Waals constant 'a' is a measure of the force of attraction between gas molecules. The higher the value of 'a', the more easily the gas is liquefied. NH3 has the highest value (4.17).
Q136mcq
The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is
a.
16 cm
Correct Answer
b.
13.2 cm
c.
12.5 cm
d.
8 cm
Step-by-Step AI Explanation
Verified Method
Open pipe f_o = v/2L_o. Closed pipe 3rd harmonic f_c = 3v/4L_c. Equating: v/2L_o = 3v/4L_c. L_o = 2/3 * L_c = 2/3 * 20 = 40/3 = 13.33cm. *Wait, re-evaluating*: If 3rd harmonic of closed is 3v/4L, and fundamental of open is v/2L: v/2L_o = 3v/4L_c => L_o = (4/6)L_c = 2/3*20 = 13.33cm. Choice a (13.33 vs 13.2) is the intended match.
Q137mcq
At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth’s atmosphere? (Given: m = 2.76 x 10^-26 kg, k_B = 1.38 x 10^-23 J/K, v_esc = 11.2 km/s)
a.
1.254 x 10^4 K
b.
2.508 x 10^4 K
c.
5.016 x 10^4 K
d.
8.360 x 10^4 K
Correct Answer
Step-by-Step AI Explanation
Verified Method
v_rms = sqrt(3kT/m). T = (m * v^2) / 3k. T = (2.76e-26 * (11200)^2) / (3 * 1.38e-23) = 8.36e4 K.
Q138mcq
The efficiency of an ideal heat engine working between the freezing point and boiling point of water, is
An inductor 20 mH, a capacitor 100 uF and a resistor 50 Ohm are connected in series across a source of emf, V = 10 sin 314 t. The power loss in the circuit is
a.
1.13 W
b.
0.79 W
Correct Answer
c.
2.74 W
d.
0.43 W
Step-by-Step AI Explanation
Verified Method
X_L = wL = 314 * 0.02 = 6.28 Ohm. X_C = 1/(wC) = 1/(314 * 10^-4) = 31.8 Ohm. Z = sqrt(R^2 + (X_L-X_C)^2) = sqrt(50^2 + (6.28-31.8)^2) = sqrt(2500 + 651) = 56.1 Ohm. I_rms = (V_peak/sqrt(2)) / Z = (10/sqrt(2)) / 56.1 = 0.126 A. Power = I_rms^2 * R = (0.126)^2 * 50 = 0.79 W.
Q142mcq
A thin diamagnetic rod is placed vertically between the poles of an electromagnet. When the current in the electromagnet is switched on, then the diamagnetic rod is pushed up, out of the horizontal magnetic field. Hence the rod gains gravitational potential energy. The work required to do this comes from
a.
the induced electric field due to the changing magnetic field
b.
the current source
Correct Answer
c.
the lattice structure of the material of the rod
d.
the magnetic field
Step-by-Step AI Explanation
Verified Method
Since a diamagnetic substance is repelled by a magnetic field, work must be done against the magnetic force to push it up. This energy is supplied by the electrical source powering the electromagnet.
Q142mcq
A thin diamagnetic rod is placed vertically between the poles of an electromagnet. When the current in the electromagnet is switched on, then the diamagnetic rod is pushed up. The work required to do this comes from
a.
the induced electric field due to the changing magnetic field
b.
the current source
Correct Answer
c.
the lattice structure of the material of the rod
d.
the magnetic field
Step-by-Step AI Explanation
Verified Method
The energy required to do the work against gravity for the diamagnetic substance being pushed out of the field is supplied by the current source powering the electromagnet.
Q143mcq
Current sensitivity of a moving coil galvanometer is 5 div/mA and its voltage sensitivity (angular deflection per unit voltage applied) is 20 div/V. The resistance of the galvanometer is
a.
500 Ohm
b.
40 Ohm
c.
250 Ohm
Correct Answer
d.
25 Ohm
Step-by-Step AI Explanation
Verified Method
Voltage sensitivity = Current sensitivity / Resistance. R = Current Sensitivity / Voltage Sensitivity = 5 div/mA / 20 div/V = 5 div / (10^-3 A) / 20 div / V = 5000 / 20 = 250 Ohm.
Q143mcq
Current sensitivity of a moving coil galvanometer is 5 div/mA and its voltage sensitivity (angular deflection per unit voltage applied) is 20 div/V. The resistance of the galvanometer is
a.
500 Ω
Correct Answer
b.
40 Ω
c.
250 Ω
d.
25 Ω
Step-by-Step AI Explanation
Verified Method
Voltage sensitivity = Current sensitivity / Resistance. Therefore, Resistance = Current sensitivity / Voltage sensitivity = 5 div/mA / 20 div/V = (5/10^-3) / 20 = 5000 / 20 = 250 Ω. Re-calculating: 5 div/10^-3 A = 5000 div/A. R = (5000 div/A) / (20 div/V) = 250 Ω.
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A moving block having mass m, collides with another stationary block having mass 4m. The lighter block comes to rest after collision. When the initial velocity of the lighter block is v, then the value of coefficient of restitution (e) will be
a.
0.4
b.
0.5
c.
0.8
d.
0.25
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Three objects, A: (a solid sphere), B: (a thin circular disk) and C: (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed ω about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation
a.
WA > WC > WB
b.
WC > WB > WA
c.
WB > WA > WC
d.
WA > WB > WC
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Unpolarised light is incident from air on a plane surface of a material of refractive index μ. At a particular angle of incidence i, it is found that the reflected and refracted rays are perpendicular to each other. Which of the following options is correct for this situation?
a.
i = tan^-1(1/μ)
b.
Reflected light is polarised with its electric vector parallel to the plane of incidence
c.
i = sin^-1(1/μ)
d.
Reflected light is polarised with its electric vector perpendicular to the plane of incidence
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In Young’s double slit experiment the separation d between the slits is 2 mm, the wavelength λ of the light used is 5896 Å and distance D between the screen and slits is 100 cm. It is found that the angular width of the fringes is 0.20°. To increase the fringe angular width to 0.21° (with same λ and D) the separation between the slits needs to be changed to
a.
1.7 mm
b.
1.8 mm
c.
2.1 mm
d.
1.9 mm
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A set of ‘n’ equal resistors, of value ‘R’ each, are connected in series to a battery of emf ‘E’ and internal resistance ‘R’. The current drawn is I. Now, the ‘n’ resistors are connected in parallel to the same battery. Then the current drawn from battery becomes 10 I. The value of ‘n’ is
a.
9
b.
10
c.
20
d.
11
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A set of ‘n’ equal resistors, of value ‘R’ each, are connected in series to a battery of emf ‘E’ and internal resistance ‘R’. The current drawn is I. Now, the ‘n’ resistors are connected in parallel to the same battery. Then the current drawn from battery becomes 10 I. The value of ‘n’ is
a.
9
b.
10
c.
20
d.
11
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Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by Δl on applying a force F, how much force is needed to stretch the second wire by the same amount?
a.
F
b.
9 F
c.
4 F
d.
6 F
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A sample of 0.1 g of water at 100°C and normal pressure (1.013 × 10^5 Nm^-2) requires 54 cal of heat energy to convert to steam at 100°C. If the volume of the steam produced is 167.1 cc, the change in internal energy of the sample, is
a.
84.5 J
b.
104.3 J
c.
42.2 J
d.
208.7 J
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A small sphere of radius ‘r’ falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to
a.
r^4
b.
r^3
c.
r^5
d.
r^2
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The power radiated by a black body is P and it radiates maximum energy at wavelength λ0. If the temperature of the black body is now changed so that it radiates maximum energy at wavelength 3/4 λ0, the power radiated by it becomes nP. The value of n is
a.
256/81
b.
4/3
c.
81/256
d.
3/4
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A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is 20 m/s^2 at a distance of 5 m from the mean position. The time period of oscillation is
a.
1 s
b.
2π s
c.
2 s
d.
π s
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A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of 27°C two successive resonances are produced at 20 cm and 73 cm of column length. If the frequency of the tuning fork is 320 Hz, the velocity of sound in air at 27°C is
a.
300 m/s
b.
330 m/s
c.
350 m/s
d.
339 m/s
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When the light of frequency 2v0 (where v0 is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is v1. When the frequency of the incident radiation is increased to 5v0, the maximum velocity of electrons emitted from the same plate is v2. The ratio of v1 to v2 is
a.
2 : 1
b.
1 : 2
c.
4 : 1
d.
1 : 4
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When the light of frequency 2v₀ (where v₀ is threshold frequency) is incident on a metal plate, the maximum velocity of electrons emitted is v₁. When the frequency of the incident radiation is increased to 5v₀, the maximum velocity of electrons emitted from the same plate is v₂. The ratio of v₁ to v₂ is
a.
2 : 1
b.
1 : 2
c.
4 : 1
d.
1 : 4
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For a radioactive material, half-life is 10 minutes. If initially there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is
a.
15
b.
20
c.
30
d.
10
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For a radioactive material, half -life is 10 minutes. If initially there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is
a.
15
b.
20
c.
30
d.
10
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An electron of mass m with an initial velocity →V = V₀î (V₀ > 0) enters an electric field →E = -E₀î (E₀ = constant > 0) at t = 0. If λ₀ is its de-Broglie wavelength initially, then its de-Broglie wavelength at time t is
a.
λ₀
b.
(λ₀) / (1 + (eE₀t / mV₀))
c.
λ₀t
d.
λ₀(1 + (eE₀t / mV₀))
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A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (Kt) as well as rotational kinetic energy (Kr) simultaneously. The ratio Kt : (Kt + Kr) for the sphere is
a.
2 : 5
b.
7 : 10
c.
10 : 7
d.
5 : 7
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If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct?
a.
‘g’ on the Earth will not change.
b.
Raindrops will fall faster.
c.
Time period of a simple pendulum on the Earth would decrease.
d.
Walking on the ground would become more difficult.
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A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere?
a.
Angular momentum
b.
Angular velocity
c.
Rotational kinetic energy
d.
Moment of inertia
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An EM wave is propagating in a medium with a velocity V = Vî. The instantaneous oscillating electric field of this EM wave is along the +y axis. Then the direction of the oscillating magnetic field of the EM wave will be along:
a.
- x direction
b.
- z direction
c.
- y direction
d.
+ z direction
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An em wave is propagating in a medium with a velocity →V = Vî. The instantaneous oscillating electric field of this em wave is along +y axis. Then the direction of oscillating magnetic field of the em wave will be along
a.
– x direction
b.
– z direction
c.
– y direction
d.
+ z direction
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A block of mass m is placed on a smooth inclined wedge ABC of inclination θ as shown in the figure. The wedge is given an acceleration ‘a’ towards the right. The relation between a and θ for the block to remain stationary on the wedge is:
a.
a = g tan θ
b.
a = g / cos θ
c.
a = g cos θ
d.
a = g / sin θ
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A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and the zero of the circular scale division coincides with 25 divisions above the reference level. If the screw gauge has a zero error of – 0.004 cm, the correct diameter of the ball is:
a.
0.529 cm
b.
0.521 cm
c.
0.053 cm
d.
0.525 cm
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A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field E. Due to the force qE, its velocity increases from 0 to 6 m/s in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively:
a.
1.5 m/s, 3 m/s
b.
2 m/s, 4 m/s
c.
1 m/s, 3.5 m/s
d.
1 m/s, 3 m/s
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