Physics
- A full wave rectifier circuit with diodes (D_1) and (D_2) is shown in the figure. If input supply voltage V_in = 220(100π t) volt, then at t = 15 msec Answer: 1. D₁ is forward biased, D₂ is reverse biased or 2. D₁ is reverse biased, D₂ is forward biased Key idea: in a centre-tapped full-wav... 1
- The intensity of transmitted light when a polaroid sheet, placed between two crossed polaroids at 22.5^° from the polarization axis of one of the polaroid, is (I_0 is the intensity of polarised light after passing through the first polaroid): Answer: 3. I₀/8 Key idea: apply Malus's law, I=I₀cos²θ , at each polaroid. The middle sheet is at 22.5^° to the first, and 90^°-22.5^°=67.5^... 1
- Two identical point masses P and Q, suspended from two separate massless springs of spring constants k_1 and k_2, respectively, oscillate vertically. If their maximum speeds are the same, the ratio (A_Q/A_P) of the amplitude A_Q of mass Q to the ampl… Answer: 4. √(k₁/k₂) Key idea: the maximum speed in SHM is v_max=Aω=A√(k/m) . Masses are identical and v_max is the same, so A_P√(k₁)=A_Q√(k₂... 1
- A pipe open at both ends has a fundamental frequency f in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to : Answer: 2. f Key idea: an open pipe of length L has fundamental f=v/2L ; a pipe closed at one end of length l has fundamental v/4l . Dipping... 1
- A physical quantity P is related to four observations a, b, c and d as follows:P = a^3b^2 / c√(d)The percentage errors of measurement in a, b, c and d are 1%, 3%, 2%, and 4% respectively. The percentage error in the quantity P is Answer: 3. 13% Key idea: for P=a³b²/csqrt d , the maximum percentage error is the sum of (power × percentage error) of each quantity. Δ P/P×... 1
- Two gases A and B are filled at the same pressure in separate cylinders with movable pistons of radius r_A and r_B, respectively. On supplying an equal amount of heat to both the systems reversibly under constant pressure, the pistons of gas A and B… Answer: 2. 3/4 Key idea: at constant pressure, Q=Δ U+W with W=pΔ V . The heat supplied and Δ U are the same for both gases, so W is equal. W... 1
- A model for quantized motion of an electron in a uniform magnetic field B states that the flux passing through the orbit of the electron is n(h/e) where n is an integer, h is Planck's constant and e is the magnitude of electron's charge. According to… Answer: 2. he/2π m Key idea: the electron moves in a circle in the field, and the given flux quantization fixes the orbit area. From evB=mv²... 1
- A particle of mass m is moving around the origin with a constant force F pulling it towards the origin. If Bohr model is used to describe its motion, the radius r of the n^th orbit and the particle's speed v in the orbit depend on n as Answer: 3. r ∝ n^(2/3);\ v ∝ n^(1/3) Key idea: apply Newton's second law with the constant force as the centripetal force, together with Boh... 1
- A constant voltage of 50 V is maintained between the points A and B of the circuit shown in the figure. The current through the branch CD of the circuit is : Answer: 2. 2.0 A Key idea: C and D are joined by a wire, so they are at the same potential. The circuit becomes two parallel pairs in series... 1
- A wire of resistance R is cut into 8 equal pieces. From these pieces two equivalent resistances are made by adding four of these together in parallel. Then these two sets are added in series. The net effective resistance of the combination is : Answer: 3. R/16 Key idea: cutting a wire into equal parts divides its resistance equally. Each piece has resistance R/8 . Four in parallel g... 1
- De-Broglie wavelength of an electron orbiting in the n = 2 state of hydrogen atom is close to (Given Bohr radius = 0.052 nm) Answer: 2. 0.67 nm Key idea: Bohr's quantization 2π r_n=nλ (electron wave fits the orbit). Radius of the n=2 orbit: r₂=n²a₀=4×0.052=0.208 nm... 1
- A photon and an electron (mass m) have the same energy E. The ratio ≤ft(λ_photon/λ_electron) of their de Broglie wavelengths is: (c is the speed of light) Answer: 3. c√(2m/E) Key idea: λ=h/p , with different momentum-energy relations for photon and electron. Photon: E=pc⇒λ_ph=hc/E . Electron: E... 1
- Which of the following options represent the variation of photoelectric current with property of light shown on the x-axis?A. Photoelectric current vs Intensity of light: straight line through origin risingB. Photoelectric current vs Intensity of lig… Answer: 1. A only Key idea: at a fixed frequency above the threshold, the photoelectric current is directly proportional to the intensity. A... 1
- To an ac power supply of 220 V at 50 Hz, a resistor of 20 Ω, a capacitor of reactance 25 Ω and an inductor of reactance 45 Ω are connected in series. The corresponding current in the circuit and the phase angle between the current and the voltage is,… Answer: 2. 7.8 A and 45^° Key idea: in a series LCR circuit, Z=√(R²+(X_L-X_C)²) and tanφ=X_L-X_C/R . X_L-X_C=45-25=20\ Ω, Z=√(20²+20²)=20sqr... 1
- A parallel plate capacitor made of circular plates is being charged such that the surface charge density on its plates is increasing at a constant rate with time. The magnetic field arising due to displacement current is : Answer: 3. non-zero everywhere with maximum at the imaginary cylindrical surface connecting peripheries of the plates Key idea: a changing e... 1
- The plates of a parallel plate capacitor are separated by d. Two slabs of different dielectric constant K_1 and K_2 with thickness 3/8d and d/2, respectively are inserted in the capacitor. Due to this, the capacitance becomes two times larger than wh… Answer: 1. 2.66 Key idea: for slabs inserted in a capacitor, C=ε₀A/d-t₁-t₂+t₁/K₁+t₂/K₂ . Here t₁=3/8d , t₂=1/2d , and C=2C₀ , so the denomin... 1
- Two identical charged conducting spheres A and B have their centres separated by a certain distance. Charge on each sphere is q and the force of repulsion between them is F. A third identical uncharged conducting sphere is brought in contact with sph… Answer: 4. 3F/8 Key idea: identical conducting spheres share charge equally on contact. Third sphere touches A: A and C each have q/2 . Then... 1
- An electric dipole with dipole moment 5×10^-6 Cm is aligned with the direction of a uniform electric field of magnitude 4×10^5 N/C. The dipole is then rotated through an angle of 60^° with respect to the electric field. The change in the potential en… Answer: 2. 1.0 J Key idea: potential energy of a dipole is U=-pEcosθ . Initially θ=0^° and then 60^° : Δ U=pE(cos0^°-cos60^°)=5×10⁻⁶×4×10⁵×1... 1
- Consider the diameter of a spherical object being measured with the help of a Vernier callipers. Suppose its 10 Vernier Scale Divisions (V.S.D.) are equal to its 9 Main Scale Divisions (M.S.D.). The least division in the M.S. is 0.1 cm and the zero o… Answer: 3. 4.98 cm Key idea: reading = MSR + (VSR × least count) - zero error. 10 VSD = 9 MSD, so the least count =1 MSD -1 VSD =0.1-0.09=0.... 1
- A body weighs 48 N on the surface of the earth. The gravitational force experienced by the body due to the earth at a height equal to one-third the radius of the earth from its surface is : Answer: 2. 27 N Key idea: weight at height h varies as 1/(R+h)² . F=48(R/R+R/3)²=48×(3/4)²=48×frac916=27\ mathrm N 1
- The radius of Martian orbit around the Sun is about 4 times the radius of the orbit of Mercury. The Martian year is 687 Earth days. Then which of the following is the length of 1 year on Mercury ? Answer: 1. 88 earth days Key idea: Kepler's third law, T²∝ r³ . fracT_MarsT_Mercury=(fracr_Marsr_Mercury)^(3/2)=4^(3/2)=8 T_Mercury=687/8≈86... 1
- In some appropriate units, time (t) and position (x) relation of a moving particle is given by t = x^2 + x. The acceleration of the particle is Answer: 2. -2/(2x+1)³ Key idea: differentiate t(x) to get velocity, then use a=v dv/dx . dt/dx=2x+1⇒ v=dx/dt=1/2x+1 a=vdv/dx=1/2x+1·(-2/(2x+... 1
- Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of 60 km/h in the direction X to Y notices that a bus goes past her every 30 minutes in the direction… Answer: 4. 15 min, 120 km/h Key idea: buses in one direction are spaced vT apart. The girl meets them at the rate set by the relative speed.... 1
- An oxygen cylinder of volume 30 litre has 18.20 moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheric pressure at temperature 27^°C. The mass of the oxygen withdrawn from the cylinder is nearly… Answer: 3. 0.116 kg Key idea: use PV=nRT for the gas left, then subtract from the initial moles. The gauge pressure must be converted to abs... 1