Physics
- The bulk modulus of a spherical object is 'B'. If it is subjected to uniform pressure 'p', the fractional decrease in radius is : Answer: 3. p/3B Key idea: B=p/Δ V/V , and for a sphere V∝ r³ , so Δ V/V=3Δ r/r . Δ r/r=1/3Δ V/V=p/3B . 1
- A spherical black body with a radius of 12 cm radiates 450 watt power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watt would be : Answer: 3. 1800 Key idea: power radiated P=σ AT⁴∝ r²T⁴ . Radius halved gives factor 1/4 ; temperature doubled gives factor 2⁴=16 . P'=450×1/... 1
- Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities ω_1 and ω_2. They are brought into contact face to face coinciding the axis of rotation. The e… Answer: 1. 1/4 I(ω₁-ω₂)² Key idea: angular momentum is conserved when the discs join. Iω₁+Iω₂=2Iω⇒ω=ω₁+ω₂/2 . Loss =1/2Iω₁²+1/2Iω₂²-1/2(2I)ω... 1
- Which of the following statements are correct ?(a) Centre of mass of a body always coincides with the centre of gravity of the body.(b) Centre of mass of a body is the point at which the total gravitational torque on the body is zero.(c) A couple on… Answer: 4. (b) and (d) Key idea: check each statement. (a) False: centre of mass and centre of gravity coincide only in a uniform gravitatio... 1
- A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N ? Answer: 2. 25 rad/s ² Key idea: τ=Iα , with τ=FR and I=MR² for a hollow cylinder. τ=30×0.4=12 N m, I=3×0.4²=0.48 kg m ² . α=12/0.48=25 rad/s... 1
- Thermodynamic processes are indicated in the following diagram.Match the following :Column-1: P. Process I; Q. Process II; R. Process III; S. Process IVColumn-2: a. Adiabatic; b. Isobaric; c. Isochoric; d. Isothermal Answer: 1. P → c, Q → a, R → d, S → b Key idea: identify each process from the P-V diagram. I: vertical line, volume constant, isochoric (c)... 1
- Radioactive material 'A' has decay constant '8λ' and material 'B' has decay constant 'λ'. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material 'B' to that 'A' will be 1/e ? Answer: 1. 1/7λ Key idea: N=N₀e^(-λ t) for each material, and take the ratio of the two. N_A=N₀e^(-8λ t) , N_B=N₀e^(-λ t) . Then N_A/N_B=e^(... 1
- The resistance of a wire is 'R' ohm. If it is melted and stretched to 'n' times its original length, its new resistance will be : Answer: 2. n²R Key idea: melting does not change the volume, so Al stays constant. If length becomes nl , area becomes A/n . Resistance R=ρl... 1
- The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (Kelvin) and mass m, is : Answer: 1. h/√(3mkT) Key idea: a thermal neutron has average kinetic energy 3/2kT , and λ=h/p=h/√(2mK) . λ=h/√(2m·3/2kT)=h/√(3mkT) . 1
- In an electromagnetic wave in free space the root mean square value of the electric field is E_rms = 6 V/m. The peak value of the magnetic field is : Answer: 1. 2.83×10⁻⁸ T Key idea: peak value =sqrt2× rms value, and B₀=E₀/c . E₀=6sqrt2=8.49 V/m. B₀=8.49/3×10⁸=2.83×10⁻⁸ T. 1
- The given electrical network is equivalent to : Answer: 2. NOR gate Key idea: trace the logic step by step. First gate is a NOR: output A+B . Second gate is a NOR with both inputs joined,... 1
- In a common emitter transistor amplifier the audio signal voltage across the collector is 3 V. The resistance of collector is 3 kΩ. If current gain is 100 and the base resistance is 2 kΩ, the voltage and power gain of the amplifier is : Answer: 2. 150 and 15000 Key idea: in a common emitter amplifier, voltage gain A_v=βR_C/R_B and power gain =β A_v . A_v=100×3\ kΩ/2\ kΩ=150... 1
- Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will : Answer: 1. move towards each other. Key idea: the only force between the two astronauts is their mutual gravitational attraction. In free sp... 1
- An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current 'I' along the same direction is shown in Fig. Magnitude of force per unit length on the middle wire 'B' is given by : Answer: 3. μ₀ i²/√(2)π d Key idea: parallel wires carrying current in the same direction attract each other, each pair giving a force per un... 1
- Young's double slit experiment is first performed in air and then in a medium other than air. It is found that 8^th bright fringe in the medium lies where 5^th dark fringe lies in air. The refractive index of the medium is nearly : Answer: 3. 1.78 Key idea: compare fringe positions using bright fringe y_n=nλ D/d and dark fringe y_n=(2n-1)λ D/2d . In air, 5th dark fringe... 1
- Two cars moving in opposite directions approach each other with speed of 22 m/s and 16.5 m/s respectively. The driver of the first car blows a horn having a frequency 400 Hz. The frequency heard by the driver of the second car is [velocity of sound 3… Answer: 3. 448 Hz Key idea: Doppler effect with source and observer approaching: f'=fv+v_o/v-v_s . f'=400×340+16.5/340-22=400×356.5/318≈448... 1
- Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K_1 and K_2. The thermal conductivity of the composite rod will be : Answer: 4. K₁+K₂/2 Key idea: the two rods are side by side, so heat flows through them in parallel, and the conductances add. Let each rod h... 1
- If an electron in a hydrogen atom jumps from the 3rd orbit to the 2nd orbit, it emits a photon of wavelength λ. When it jumps from the 4th orbit to the 3rd orbit, the corresponding wavelength of the photon will be Answer: 2. 20/7λ Use dfrac1λ=R(dfrac1n₁²-dfrac1n₂²) . 3 to 2: dfrac1λ=R(1/4-1/9)=5R/36 . 4 to 3: dfrac1λ'=R(1/9-dfrac116)=7R/144 . λ'/λ=5/36... 1
- The half-life of a radioactive substance is 30 minutes. The time (in minutes) taken between 40% decay and 85% decay of the same radioactive substance is Answer: 3. 60 Use N=N₀(1/2)^(t/T) and compare the remaining fractions. 40% decayed means 60% remains; 85% decayed means 15% remains. Ratio o... 1
- Photons with energy 5 eV are incident on a cathode C in a photoelectric cell. The maximum energy of emitted photoelectrons is 2 eV. When photons of energy 6 eV are incident on C, no photoelectrons will reach the anode A, if the stopping potential of… Answer: 3. -3 V Einstein's equation: K_max=hν-φ . 5 eV photon, K_max=2 eV, so φ=3 eV. 6 eV photon: K_max=6-3=3 eV. To stop all electrons the... 1
- Electrons of mass m with de-Broglie wavelength λ fall on the target in an X-ray tube. The cutoff wavelength (λ_0) of the emitted X-ray is Answer: 4. λ₀=2mcλ²/h The cutoff wavelength corresponds to the whole kinetic energy K of the electron turning into one photon: λ₀=hc/K . de... 1
- What is the output Y in the following circuit, when all the three inputs A, B, C are first 0 and then 1? Answer: 2. 1, 0 Gate P is an AND gate on A and B; gate Q is a NAND gate whose inputs are P's output and C. So Y=(A· B)· C . A = B = C = 0: P... 1
- The given circuit has two ideal diodes connected as shown in the figure below. The current flowing through the resistance R_1 will be Answer: 4. 2.5 A An ideal diode conducts only when forward biased. From the figure, the battery drives current through R₁ and then to the tw... 1
- For CE transistor amplifier, the audio signal voltage across the collector resistance of 2 kΩ is 4 V. If the current amplification factor of the transistor is 100 and the base resistance is 1 kΩ, then the input signal voltage is Answer: 1. 20 mV In a CE amplifier, V_out=I_CR_C and I_C=β I_B ; input voltage is V_in=I_BR_B . I_C=4/2000=2 mA. I_B=I_C/β=2\ mA/100=20\ μA... 1