Physics
- Two cars P and Q start from a point at the same time in a straight line and their positions are represented by x_P(t)=at+bt^2 and x_Q(t)=ft-t^2. At what time do the cars have the same velocity? Answer: 3. f-a/2(1+b) Velocity is the derivative of position; equate the two velocities. v_P=a+2bt ; v_Q=f-2t . a+2bt=f-2t⇒ 2t(b+1)=f-a . t=... 1
- In the given figure, a=15 m/s^2 represents the total acceleration of a particle moving in the clockwise direction in a circle of radius R=2.5 m at a given instant of time. The speed of the particle is Answer: 2. 5.7 m/s The total acceleration has a radial (centripetal) part v²/R and a tangential part. From the figure, a makes 30^° with the... 1
- A rigid ball of mass m strikes a rigid wall at 60° and gets reflected without loss of speed as shown in the figure below. The value of impulse imparted by the wall on the ball will be Answer: 4. mV The wall is smooth, so only the component of velocity perpendicular to the wall changes; the parallel component stays the same... 1
- A linear aperture whose width is 0.02 cm is placed immediately in front of a lens of focal length 60 cm. The aperture is illuminated normally by a parallel beam of wavelength 5×10^-5 cm. The distance of the first dark band of the diffraction pattern… Answer: 3. 0.15 cm For the first dark band in single-slit diffraction, asinθ=λ . sinθ=dfrac5×10⁻⁵0.02=2.5×10⁻³ , a small angle. Distance on... 1
- Planck's constant (h), speed of light in vacuum (c) and Newton's gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length? Answer: 4. frac√(hG)c^(3/2) Write the dimensions: [h]=ML²T⁻¹ , [c]=LT⁻¹ , [G]=M⁻¹L³T⁻² . Length has the dimension of √(Gh/c³) (the Planck le... 1
- Two rotating bodies A and B of masses m and 2m with moments of inertia I_A and I_B (I_B>I_A) have equal kinetic energy of rotation. If L_A and L_B be their angular momenta respectively, then Answer: 2. L_B>L_A Express angular momentum through kinetic energy: K=L²/2I , so L=√(2IK) . The kinetic energies are equal, so L∝sqrt I . Si... 1
- A bullet of mass 10 g moving horizontally with a velocity of 400 m s^-1 strikes a wooden block of mass 2 kg which is suspended by a light inextensible string of length 5 m. As a result, the centre of gravity of the block is found to rise a vertical d… Answer: 2. 120 m s ⁻¹ Use energy for the swing of the block and momentum conservation for the collision. Block after impact: v=√(2gh)=√(2×10... 1
- Two identical balls A and B having velocities of 0.5 m/s and -0.3 m/s respectively collide elastically in one dimension. The velocities of B and A after the collision respectively will be Answer: 1. 0.5 m/s and -0.3 m/s For an elastic head-on collision between two identical masses, the bodies simply exchange velocities. (Momen... 1
- A particle moves from a point (-2 i+5 j) to (4 j+3 k) when a force of (4 i+3 j) N is applied. How much work has been done by the force? Answer: 2. 5 J Work =vec F·vec d , where vec d is the displacement. vec d=(4hat j+3hat k)-(-2hat i+5hat j)=2hat i-hat j+3hat k . W=(4hat i+3... 1
- A filament bulb (500 W, 100 V) is to be used in a 230 V main supply. When a resistance R is connected in series, it works perfectly and the bulb consumes 500 W. The value of R is Answer: 2. 26 Ω The bulb rated 500 W at 100 V must carry its rated current for full power. Rated current I=P/V=500/100=5 A. Supply 230 V; bu... 1
- The potential difference (V_A-V_B) between the points A and B in the given figure is Answer: 3. +9 V Move from A to B and add the potential change across each element. Resistor 2 Ω in the direction of current: drop of 2×2=4 V... 1
- A uniform magnetic field is restricted within a region of radius r. The magnetic field changes with time at a rate d B/dt. Loop 1 of radius R>r encloses the region r and loop 2 of radius R is outside the region of magnetic field as shown in the figur… Answer: 3. -dvec B/dtπ r² in loop 1 and zero in loop 2 Induced emf is -dΦ/dt , and flux counts only the area where the field exists. Loop 1... 1
- The potential differences across the resistance, capacitance and inductance are 80 V, 40 V and 100 V respectively in an L-C-R circuit. The power factor of this circuit is Answer: 2. 0.8 Power factor cosφ=V_R/V , where V is the supply voltage. V_L-V_C=100-40=60 V. V=√(V_R²+(V_L-V_C)²)=√(80²+60²)=100 V. cosφ=80/... 1
- Which of the following combinations should be selected for better tuning of an L-C-R circuit used for communication? Answer: 2. R=15\ Ω , L=3.5 H, C=30\ μ F Good tuning means a sharp resonance, i.e. a high quality factor Q=1/R√(L/C) . Option √(L/C) ( Ω ) Q... 1
- A 100 Ω resistance and a capacitor of 100 Ω reactance are connected in series across a 220 V source. When the capacitor is 50% charged, the peak value of the displacement current is Answer: 4. 2.2 A Displacement current in the capacitor gap equals the conduction current in the circuit at every instant, so its peak is the... 1
- A parallel-plate capacitor of area A, plate separation d and capacitance C is filled with four dielectric materials having dielectric constants k_1,k_2,k_3 and k_4 as shown in the figure below. If a single dielectric material is to be used to have th… Answer: 2. 2/k=3/k₁+k₂+k₃+1/k₄ The upper half (thickness d/2 ) has three dielectrics side by side, each of area A/3 , so they are in paralle... 1
- An electric dipole is placed at an angle of 30° with an electric field intensity 2×10^5 N/C. It experiences a torque equal to 4 N m. The charge on the dipole, if the dipole length is 2 cm, is Answer: 1. 2 mC Torque on a dipole: τ=pEsinθ , with p=q l . 4=q(0.02)(2×10⁵)sin30^°=q×2000 q=4/2000=2×10⁻³ C =2 mC. Option (1). 1
- Starting from the centre of the earth having radius R, the variation of g (acceleration due to gravity) is shown by Answer: 1. graph (1) Inside the earth g is proportional to the distance from the centre; outside it falls as 1/r² . For r For r>R : g=GM/r²... 1
- A satellite of mass m is orbiting the earth (of radius R) at a height h from its surface. The total energy of the satellite in terms of g_0, the value of acceleration due to gravity at the earth's surface, is Answer: 1. -mg₀R²/2(R+h) For a satellite in orbit, total energy is half of its (negative) potential energy: E=-GMm/2(R+h) . Use g₀=GM/R² , s... 1
- A given sample of an ideal gas occupies a volume V at a pressure P and absolute temperature T. The mass of each molecule of the gas is m. Which of the following gives the density of the gas? Answer: 1. Pm/(kT) Density ρ=mass/volume . Use the ideal gas law in terms of the number of molecules N : PV=NkT . Mass =Nm , so ρ=Nm/V=Pm/kT... 1
- A long wire carrying a steady current is bent into a circular loop of one turn. The magnetic field at the centre of the loop is B. It is then bent into a circular coil of n turns. The magnetic field at the centre of this coil of n turns will be Answer: 1. n²B Field at the centre of a circular coil: B=μ₀ N I/2r . One turn: wire length L=2π r , so B=μ₀ I/2r . n turns from the same wir... 1
- An electron is moving in a circular path under the influence of a transverse magnetic field of 3.57×10^-2 T. If the value of e/m is 1.76×10^11 C/kg, the frequency of revolution of the electron is Answer: 4. 1 GHz An electron in a magnetic field circles with frequency f=eB/2π m=1/2π·e/m· B . f=frac1.76×10¹¹×3.57×10⁻²2×3.14=frac6.28×10⁹... 1
- A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium state. The energy required to rotate it by 60° is W. Now the torque required to keep the magnet in this new position is Answer: 1. sqrt3W Work to rotate a magnet from equilibrium ( θ=0 ) is W=MB(1-cosθ) ; torque at angle θ is τ=MBsinθ . W=MB(1-cos60^°)=MB/2 ,... 1
- The interference pattern is obtained with two coherent light sources of intensity ratio n. In the interference pattern, the ratio I_max-I_minI_max+I_min will be Answer: 1. 2sqrt n/n+1 With intensities I₁:I₂=n (take I₁=nI₂ ), I_max=(√(I₁)+√(I₂))² and I_min=(√(I₁)-√(I₂))² . fracI_max-I_minI_max+I_min=4... 1