Physics
- If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct ? Answer: 4. 'g' on the Earth will not change. Check each statement with M_sun→ M/10 and G→10G . The Earth's g=GM_e/R_e² becomes 10 times larg... 1
- A block of mass m is placed on a smooth inclined wedge ABC of inclination θ as shown in the figure. The wedge is given an acceleration 'a' towards the right. The relation between a and θ for the block to remain stationary on the wedge is Answer: 4. a=gtanθ For the block to stay at rest on the smooth wedge accelerating right with a , in the wedge frame use a pseudo force ma on... 1
- Which one of the following statements is incorrect ? Answer: 4. Coefficient of sliding friction has dimensions of length. Check each statement. Rolling friction is smaller than sliding friction... 1
- A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere ? Answer: 4. Angular momentum The sphere is in free space, so there is no external torque and angular momentum L=Iω is conserved. When the rad... 1
- A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (K_t) as well as rotational kinetic energy (K_r) simultaneously. The ratio K_t:(K_t+K_r) for the sphere is Answer: 3. 5 : 7 For a solid sphere rolling without slipping, K_t=1/2mv² and K_r=1/2Iω²=1/2·2/5mR²·v²/R²=1/5mv² . K_t/K_t+K_r=1/2/1/2+1/5=5/... 1
- Three objects, A : (a solid sphere), B : (a thin circular disk) and C : (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed ω about their own symmetry axes. The amounts of work (W) required to bring th… Answer: 1. W_C>W_B>W_A Work needed to stop each body equals its rotational kinetic energy, W=1/2Iω² . Same M , R , ω , so W∝ I . Solid spher... 1
- A moving block having mass m, collides with another stationary block having mass 4m. The lighter block comes to rest after collision. When the initial velocity of the lighter block is v, then the value of coefficient of restitution (e) will be Answer: 3. 0.25 Momentum conservation: mv=0+4mv₂⇒ v₂=v/4 (lighter block at rest, v₁=0 ). Coefficient of restitution = relative speed of sepa... 1
- A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field E. Due to the force q E, its velocity increases from 0 to 6 m/s in one second duration. At that instant the direction of the fiel… Answer: 3. 1 m/s, 3 m/s Phase 1 (0 to 1 s): a=6\ m/s² , displacement =1/2·6·1=3 m, ending at 6 m/s. Phase 2 (1 to 3 s): the acceleration rev... 1
- A body initially at rest and sliding along a frictionless track from a height h (as shown in the figure) just completes a vertical circle of diameter AB = D. The height h is equal to Answer: 4. 5/4 D To just complete the vertical circle of radius R=D/2 , the speed at the top B must satisfy v_B²=gR . Energy conservation fr... 1
- The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom, is Answer: 3. 1 : - 1 In a Bohr orbit, kinetic energy K=ke²/2r and potential energy U=-ke²/r . Total energy E=K+U=-ke²/2r=-K . K/E=K/-K=1:-1 1
- For a radioactive material, half-life is 10 minutes. If initially there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is Answer: 1. 20 If 450 of 600 nuclei disintegrate, 150 remain, which is 1/4 of the original. N/N₀=(1/2)ⁿ=1/4⇒ n=2 half-lives. Time =2×10=20 mi... 1
- A battery consists of a variable number 'n' of identical cells (having internal resistance 'r' each) which are connected in series. The terminals of the battery are short-circuited and the current I is measured. Which of the graphs shows the correct… Answer: 1. (graph: I constant, horizontal line vs n) For n identical cells in series, total emf is nE and total internal resistance is nr .... 1
- A set of 'n' equal resistors, of value 'R' each, are connected in series to a battery of emf 'E' and internal resistance 'R'. The current drawn is I. Now, the 'n' resistors are connected in parallel to the same battery. Then the current drawn from ba… Answer: 1. 10 Series: total resistance nR+R , so I=E/(n+1)R . Parallel: total resistance R/n+R=(n+1)R/n , so I'=nE/(n+1)R . I'/I=n=10⇒ n=10 1
- A carbon resistor of (47±4.7) kΩ is to be marked with rings of different colours for its identification. The colour code sequence will be Answer: 3. Yellow - Violet - Orange - Silver Colour code digits: Yellow 4, Violet 7, Orange 3 (multiplier 10³ ), Silver ±10% , Gold ±5% . 47... 1
- When the light of frequency 2_0 (where _0 is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is v_1. When the frequency of the incident radiation is increased to 5_0, the maximum velocity of electrons emi… Answer: 1. 1 : 2 Einstein's equation: K_max=hν-hν₀ . At 2ν₀ : K₁=hν₀ . At 5ν₀ : K₂=4hν₀ . Since K=1/2mv² , v∝sqrt K : v₁/v₂=√(1/4)=1/2 Ratio... 1
- An electron of mass m with an initial velocity V=V_0 i (V_0>0) enters an electric field E=-E_0 i (E_0 = constant >0) at t = 0. If λ_0 is its de-Broglie wavelength initially, then its de-Broglie wavelength at time t is Answer: 1. λ₀/(1+eE₀/mV₀t) The electron has charge -e and the field is -E₀hat i , so the force is +eE₀hat i . It accelerates along its motio... 1
- The magnetic potential energy stored in a certain inductor is 25 mJ, when the current in the inductor is 60 mA. This inductor is of inductance Answer: 4. 13.89 H Energy stored in an inductor: U=1/2LI² . L=2U/I²=frac2×25×10⁻³(60×10⁻³)²=frac0.053.6×10⁻³≈13.89\ H 1
- An em wave is propagating in a medium with a velocity V=V i. The instantaneous oscillating electric field of this em wave is along +y axis. Then the direction of oscillating magnetic field of the em wave will be along Answer: 3. + z direction In an em wave, vec E , vec B and the direction of propagation are mutually perpendicular, and vec E×vec B points al... 1
- In the combination of the following gates the output Y can be written in terms of inputs A and B as Answer: 3. A·B+A· B Read the figure: the upper AND gate gets A and overline B ; the lower AND gate gets overline A and B . An OR gate joins... 1
- In a p-n junction diode, change in temperature due to heating Answer: 4. affects the overall V - I characteristics of p-n junction Heating changes the number of thermally generated electron-hole pairs,... 1
- The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is Answer: 1. independent of the distance between the plates. The field of one plate is σ/2ε₀ , and this acts on the charge Q of the other plat... 1
- In the circuit shown in the figure, the input voltage V_i is 20 V, V_BE = 0 and V_CE = 0. The values of I_B, I_C and β are given by Answer: 4. I_B = 40 μ A, I_C = 5 mA, β = 125 From the figure: R_B=500\ kΩ , R_C=4\ kΩ , supply 20 V, V_i=20 V, with V_BE=0 and V_CE=0 . I_B=... 1
- An electron falls from rest through a vertical distance h in a uniform and vertically upward directed electric field E. The direction of electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it throu… Answer: 1. smaller The force magnitude is eE for both particles, so a=eE/m . Fall distance h=1/2at² gives t=√(2h/a) . The electron has a muc... 1
- A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of 27°C two successive resonances are produced at 20 cm and 73 cm of column length. If the… Answer: 3. 339 m/s In a resonance tube, two successive resonances are half a wavelength apart. dfracλ2=73-20=53 cm, so λ=106 cm =1.06 m. v=f... 1