Physics
- 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 zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero err… Answer: 4. 0.529 cm Observed reading =0.5+25×0.001=0.525 cm. Zero error is -0.004 cm, so the correction is +0.004 cm. d=0.525-(-0.004)=0.529... 1
- 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… Answer: 3. 1.9 mm Angular fringe width is θ=λ/d , so θ∝1/d for fixed λ . d₂/d₁=θ₁/θ₂⇒ d₂=2×0.20/0.21≈1.9\ mm The slit separation must be dec... 1
- An astronomical refracting telescope will have large angular magnification and high angular resolution, when it has an objective lens of Answer: 2. large focal length and large diameter Angular magnification of an astronomical telescope is m=f_o/f_e , so a large objective foca... 1
- 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… Answer: 3. Reflected light is polarised with its electric vector perpendicular to the plane of incidence When reflected and refracted rays a... 1
- An object is placed at a distance of 40 cm from a concave mirror of focal length 15 cm. If the object is displaced through a distance of 20 cm towards the mirror, the displacement of the image will be Answer: 3. 36 cm away from the mirror Use the mirror formula 1/v+1/u=1/f with f=-15 cm. Case 1: u=-40 : 1/v=-dfrac115+dfrac140=-5/120⇒ v=-24... 1
- The refractive index of the material of a prism is 2 and the angle of the prism is 30^°. One of the two refracting surfaces of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face… Answer: 3. 45^° The ray retraces its path only if it strikes the silvered face normally. The prism angle is A=30^° . For a ray hitting the s... 1
- 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 o… Answer: 3. π s For SHM, a=ω²x . ω²=20/5=4⇒ω=2\ mathrmrad s⁻¹ . T=2π/ω=π\ s 1
- 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 Δ l on applying a force F, how much force is… Answer: 1. 9 F Same volume: A l=3A l₂ , so the second wire has length l₂=l/3 . From Y=F l/A Δ l , F=YAΔ l/l . F₂=Y(3A)Δ l/l/3=9·YAΔ l/l=9F 1
- The power radiated by a black body is P and it radiates maximum energy at wavelength, λ_0. If the temperature of the black body is now changed so that it radiates maximum energy at wavelength 34λ_0, the power radiated by it becomes nP. The value of n… Answer: 2. 256/81 Wien's law: λ_mT= constant, so T∝dfrac1λ_m . Stefan's law: P∝ T⁴ . New wavelength is 3/4λ₀ , so T'=4/3T . n=(4/3)⁴=256/81 1
- 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 Answer: 2. r⁵ At terminal velocity, heat is produced at the rate equal to the power of the viscous force: P=F v_t=6πη r v_t² . Terminal velo... 1
- The moment of the force, F=4 i+5 j-6 k at (2, 0, -3), about the point (2, -2, -2), is given by Answer: 4. -7hat i-4hat j-8hat k Moment (torque) about a point: vecτ=vec r×vec F , where vec r goes from the point to the point of applicati... 1
- 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 Answer: 3. 208.7 J First law: Δ U=Q-W , with W=PΔ V . Q=54×4.18≈225.7 J. Volume change: steam 167.1 cc minus water 0.1 cc, Δ V=167\ cm³=1.67... 1
- An inductor 20 mH, a capacitor 100 μF and a resistor 50 Ω are connected in series across a source of emf, V = 10 sin 314 t. The power loss in the circuit is Answer: 1. 0.79 W Power is lost only in the resistor: P=I_rms²R , with I_rms=V_rms/Z . X_L=ω L=314×0.02=6.28\ Ω ; X_C=1/ω C=dfrac1314×10⁻⁴=3... 1
- A long solenoid of diameter 0.1 m has 2×10^4 turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0A… Answer: 2. 32 μ C Key idea: charge q=ΔΦ/R (independent of the time taken). Field inside solenoid B=μ₀nI . Change: Δ B=4π×10⁻⁷×2×10⁴×4=0.032π... 1
- The x and y coordinates of the particle at any time are x = 5t - 2t^2 and y = 10t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t = 2s is : Answer: 2. - 4 m/s ² Key idea: acceleration components are second derivatives of position. a_x=d²x/dt²=-4 m/s ² , a_y=d²y/dt²=0 . Accelerati... 1
- At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere ?(Given :Mass of oxygen molecule (m) = 2.76×10^-26 kgBoltzmann's constant k_B = 1.38×10^-23 J K^-1) Answer: 3. 8.360×10⁴ K The molecules escape only if their rms speed equals the escape speed of the Earth, v_e = 11.2\ mathrmkm s⁻¹ = 1.12×10... 1
- A metallic rod of mass per unit length 0.5 kg m^-1 is lying horizontally on a smooth inclined plane which makes an angle of 30^° with the horizontal. The rod is not allowed to slide down by flowing a current through it when a magnetic field of induct… Answer: 4. 11.32 A For the rod to stay at rest on a smooth incline, the horizontal magnetic force must balance the component of weight down... 1
- 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 po… Answer: 1. the current source A static magnetic field exerts a force perpendicular to the motion of charges, so it does no net work itself.... 1
- 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 Answer: 2. 250 Ω Current sensitivity I_s=θ/I and voltage sensitivity V_s=θ/V . Since V=IG , V_s=I_s/G . G=I_s/V_s=5\ div/mA/20\ div/V=frac5\... 1
- A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is : Answer: 2. 4π/sqrt5 Key idea: in SHM v=ω√(A²-x²) and a=ω²x . At x=2 cm, A=3 cm: ω√(9-4)=ω²×2⇒ω=sqrt5/2 s ⁻¹ . T=2π/ω=4π/sqrt5 s. 1
- 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 Answer: 1. 13.2 cm Closed pipe: odd harmonics only, f_n=nv/4L . Third harmonic: f=3v/4× 20 . Open pipe fundamental: f₁=v/2L' . Equating: v/2... 1
- A U tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm above the water level on the other side. Meanwhile the water rises by… Answer: 3. 928 kg m ⁻³ Key idea: pressure at the same level in the same liquid is equal. Take points B (oil-water interface, left) and C (sa... 1
- The volume (V) of a monatomic gas varies with its temperature (T), as shown in the graph. The ratio of work done by the gas, to the heat absorbed by it, when it undergoes a change from state A to state B, is Answer: 1. 2/5 The graph is a straight line through the origin, so V∝ T : the process is at constant pressure. For a monatomic gas, W=nRΔ T... 1
- A carnot engine having an efficiency of 1/10 as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is : Answer: 1. 90 J Key idea: as a refrigerator, coefficient of performance =Q₂/W=1-η/η . η=tfrac110⇒Q₂/W=9/10/1/10=9 . Q₂=9×10=90 J absorbed fr... 1