Physics
- A spring is stretched by 5 cm by a force 10 N. The time period of the oscillations when a mass of 2 kg is suspended by it is : Answer: 4. 0.628 s Key idea: find k from the stretch, then use T=2π√(m/k) . k=F/x=10/0.05=200\ N/m T=2π√(2/200)=2π×0.1=0.628\ mathrm s . Opt... 1
- If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy. Answer: 2. [F][A][ T² ] Key idea: write energy as work = force × distance, and express the distance through acceleration and time. L = 1/2 A... 1
- A cup of coffee cools from 90°C to 80°C in t minutes, when the room temperature is 20°C. The time taken by a similar cup of coffee to cool from 80°C to 60°C at a room temperature same at 20°C is : Answer: 2. 13/5t Key idea: Newton's law of cooling in the average-temperature form: Δ T/t=k(T_avg-T₀) . First case: 10/t=k(85-20)=65k⇒ k=2/1... 1
- The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is d/2, then the viscous force acting on the ball will be : Answer: 1. Mg/2 Key idea: at constant (terminal) velocity the net force is zero: weight = buoyancy + viscous force. Volume of ball V=M/d . B... 1
- A particle is released from height S from the surface of the Earth. At a certain height its kinetic energy is three times its potential energy. The height from the surface of earth and the speed of the particle at that instant are respectively : Answer: 4. S/4, √(3gS/2) Key idea: total mechanical energy mgS is conserved (taking the surface as zero of potential energy). At height h: U... 1
- When a uranium isotope ^235_92U is bombarded with a neutron, it generates ^89_36Kr, three neutrons and : Answer: 1. ¹⁴⁴₅₆ Ba Balance mass number and atomic number. Left: ²³⁵₉₂U+¹₀n gives A=236,\ Z=92 . Right: ⁸⁹₃₆Kr+3 ¹₀n+^A_Z X . A=236-89-3=144... 1
- A charged particle having drift velocity of 7.5×10^-4 m s^-1 in an electric field of 3×10^-10 V m^-1, has a mobility in m^2 V^-1 s^-1 of : Answer: 2. 2.5×10⁶ Mobility is drift velocity per unit electric field: μ=v_d/E . μ=frac7.5×10⁻⁴3×10⁻¹⁰=2.5×10⁶\ m²V⁻¹s⁻¹ Answer: option 2. 1
- The color code of a resistance is given below :(figure: colour bands Yellow, Violet, Brown, Gold)The values of resistance and tolerance, respectively, are : Answer: 4. 470 Ω , 5% Four-band colour code: first two bands are digits, the third is the multiplier, the fourth is tolerance. Yellow = 4, V... 1
- Which of the following graph represents the variation of resistivity (ρ) with temperature (T) for copper ? Answer: 3. graph (3) For a metal like copper, resistivity rises with temperature because lattice vibrations scatter electrons more: ρ=ρ₀[1+α... 1
- A resistance wire connected in the left gap of a metre bridge balances a 10 Ω resistance in the right gap at a point which divides the bridge wire in the ratio 3 : 2. If the length of the resistance wire is 1.5 m, then the length of 1 Ω of the resist… Answer: 2. 1.0×10⁻¹ m Metre bridge balance: X/10=l/100-l=3/2 . X=15\ Ω This 15 Ω is the resistance of the whole 1.5 m wire. Length per ohm:... 1
- An electron is accelerated from rest through a potential difference of V volt. If the de Broglie wavelength of the electron is 1.227×10^-2 nm, the potential difference is : Answer: 4. 10⁴ V de Broglie wavelength of an electron accelerated through V volts: λ=1.227/sqrt V nm. Given λ=1.227×10⁻² nm: sqrt V=frac1.22... 1
- A series LCR circuit is connected to an ac voltage source. When L is removed from the circuit, the phase difference between current and voltage is π/3. If instead C is removed from the circuit, the phase difference is again π/3 between current and vo… Answer: 3. 1.0 With L removed, the circuit is RC: tanφ=X_C/R . With C removed, it is RL: tanφ=X_L/R . Both phase angles are π/3 , so X_C=X_L... 1
- For the logic circuit shown, the truth table is :(figure: A and B each pass through a NOT gate; both outputs feed a NOR-type gate (OR gate with output bubble) giving Y) Answer: 1. A B Y: 00->0, 01->0, 10->0, 11->1 From the figure, each input goes through a NOT gate, and the outputs feed a NOR gate (OR with a... 1
- The capacitance of a parallel plate capacitor with air as medium is 6 μF. With the introduction of a dielectric medium, the capacitance becomes 30 μF. The permittivity of the medium is :(ε_0 = 8.85×10^-12 C^2 N^-1 m^-2) Answer: 3. 0.44×10⁻¹⁰ C ² N ⁻¹ m ⁻² Capacitance with a dielectric of relative permittivity K is C=KC₀ . So K=30/6=5 Permittivity of the medi... 1
- A short electric dipole has a dipole moment of 16×10^-9 C m. The electric potential due to the dipole at a point at a distance of 0.6 m from the centre of the dipole, situated on a line making an angle of 60^° with the dipole axis is :≤ft(1/4πε_0 = 9… Answer: 2. 200 V Potential of a short dipole: V=1/4πε₀pcosθ/r² . V=frac9×10⁹×16×10⁻⁹×cos60^°(0.6)²=144×0.5/0.36=200\ V Answer: option 2. 1
- A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s. The height of the tower is : (g = 10 m/s^2) Answer: 4. 300 m Use v²=u²+2gh (downward motion, g positive). h=v²-u²/2g=80²-20²/2×10=6400-400/20=300\ m Answer: option 4. 1
- The average thermal energy for a mono-atomic gas is : (k_B is Boltzmann constant and T, absolute temperature) Answer: 2. 3/2k_BT A monoatomic gas molecule has only 3 translational degrees of freedom. By the equipartition law each gives 1/2k_BT . E=3×... 1
- Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (g) is : Answer: 3. g/5 Atwood machine: the heavier mass moves down, and both masses share the same acceleration. a=(m₂-m₁)g/m₁+m₂=(6-4)g/6+4=g/5 Ans... 1
- A long solenoid of 50 cm length having 100 turns carries a current of 2.5 A. The magnetic field at the centre of the solenoid is :(μ_0 = 4π×10^-7 T m A^-1) Answer: 1. 6.28×10⁻⁴ T Field inside a long solenoid: B=μ₀nI , with n turns per metre. n=100/0.5=200\ m⁻¹ B=4π×10⁻⁷×200×2.5=6.28×10⁻⁴\ T Answ... 1
- An iron rod of susceptibility 599 is subjected to a magnetising field of 1200 A m^-1. The permeability of the material of the rod is :(μ_0 = 4π×10^-7 T m A^-1) Answer: 1. 2.4π×10⁻⁴ T m A ⁻¹ Relative permeability μ_r=1+chi=1+599=600 . μ=μ₀μ_r=4π×10⁻⁷×600=2.4π×10⁻⁴\ T m A⁻¹ The magnetising field 1200... 1
- In Young's double slit experiment, if the separation between coherent sources is halved and the distance of the screen from the coherent sources is doubled, then the fringe width becomes : Answer: 3. four times Fringe width β=λ D/d . With d→ d/2 and D→2D : β'=λ(2D)/d/2=4β The fringe width becomes four times. Answer: option 3. 1
- Assume that light of wavelength 600 nm is coming from a star. The limit of resolution of telescope whose objective has a diameter of 2 m is : Answer: 1. 3.66×10⁻⁷ rad Limit of resolution of a telescope: Δθ=1.22λ/D . Δθ=frac1.22×600×10⁻⁹2=3.66×10⁻⁷\ rad Answer: option 1. 1
- Dimensions of stress are : Answer: 4. [ML⁻¹T⁻²] Stress =force/area . [stress]=frac[MLT⁻²][L²]=[ML⁻¹T⁻²] This is the same as the dimensions of pressure. Answer: option... 1
- Taking into account of the significant figures, what is the value of 9.99 m - 0.0099 m ? Answer: 2. 9.98 m For subtraction, the result keeps as many decimal places as the number with the fewest decimal places. 9.99 has 2 decimals... 1