Physics
- Increase in temperature of a gas filled in a container would lead to : Answer: 2. increase in its kinetic energy The temperature of a gas measures the average kinetic energy of its molecules. Raising the tempera... 1
- A particle moving with velocity V is acted by three forces shown by the vector triangle PQR. The velocity of the particle will : Answer: 3. remain constant In the figure the three vectors overrightarrowPQ,overrightarrowQR,overrightarrowRP are placed head to tail and fo... 1
- A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1 m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder to ke… Answer: 3. 10 rad/s The wall's normal force supplies the centripetal force: N=mω²r . Friction balances weight: μ N=mg . μ mω²r=mg⇒ω=√(g/μ r)... 1
- At a point A on the earth's surface the angle of dip, δ = +25^°. At a point B on the earth's surface the angle of dip, δ = -25^°. We can interpret that : Answer: 3. A is located in the northern hemisphere and B is located in the southern hemisphere. The angle of dip is positive (the north pole... 1
- Two similar thin equi-convex lenses, of focal length f each, are kept coaxially in contact with each other such that the focal length of the combination is F_1. When the space between the two lenses is filled with glycerin (which has the same refract… Answer: 2. 1 : 2 Two thin lenses in contact: dfrac1F₁=1/f+1/f , so F₁=f/2 . When the gap is filled with glycerin of the same index as glass,... 1
- Pick the wrong answer in the context with rainbow. Answer: 3. An observer can see a rainbow when his front is towards the sun. We pick the wrong statement. Two internal reflections give the s... 1
- In total internal reflection when the angle of incidence is equal to the critical angle for the pair of media in contact, what will be angle of refraction ? Answer: 4. 90^° At the critical angle C , Snell's law gives μ₁sin C=μ₂sin r with sin C=μ₂/μ₁ . So sin r=1 and r=90^° : the refracted ray gra... 1
- The displacement of a particle executing simple harmonic motion is given byy = A_0 + Aω t + Bω t.Then the amplitude of its oscillation is given by : Answer: 2. √(A²+B²) The constant A₀ only shifts the mean position. The oscillating part is Asinω t+Bcosω t . Write it as Csin(ω t+φ) with Cc... 1
- Average velocity of a particle executing SHM in one complete vibration is : Answer: 4. zero Average velocity =displacement/time . In one complete vibration the particle returns to its starting point, so the displacem... 1
- A small hole of area of cross-section 2 mm^2 is present near the bottom of a fully filled open tank of height 2 m. Taking g = 10 m/s^2, the rate of flow of water through the open hole would be nearly : Answer: 1. 12.6×10⁻⁶ m ³ /s By Torricelli's theorem the speed of efflux is v=√(2gh) . v=√(2×10×2)=√(40)≈6.32 m/s. Rate of flow =Av=2×10⁻⁶×6.... 1
- A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is : (α_Cu = 1.7×10^-5 K^-1 and α_Al = 2.2×10^-5 K^-1) Answer: 4. 68 cm The difference in length stays the same at all temperatures only if both rods expand by the same amount: Δ l_Cu=Δ l_Al . l_... 1
- The unit of thermal conductivity is : Answer: 4. W m ⁻¹ K ⁻¹ From Q/T=KA Δθ/L , K=(Q/t) L/A Δθ . Unit of Q/t is W, L is m, A is m ² , Δθ is K. So K has unit W m/m² K=W m⁻¹K⁻¹ . 1
- A solid cylinder of mass 2 kg and radius 4 cm is rotating about its axis at the rate of 3 rpm. The torque required to stop after 2π revolutions is : Answer: 1. 2×10⁻⁶ N m Find the angular deceleration from the rotation kinematics, then use τ=Iα . ω₀=3 rpm =3×2π/60=0.1π rad/s. Angle turned... 1
- A force F = 20 + 10y acts on a particle in y-direction where F is in newton and y in meter. Work done by this force to move the particle from y = 0 to y = 1 m is : Answer: 3. 25 J Work done by a variable force is W=∫ F dy . W=∫₀¹(20+10y) dy=[20y+5y²]₀¹=20+5=25 J. 1
- In which of the following devices, the eddy current effect is not used ? Answer: 3. electromagnet or 4. electric heater Eddy currents are induced in a conductor by a changing magnetic flux. Induction furnace: eddy... 1
- Which colour of the light has the longest wavelength ? Answer: 1. red In the visible spectrum wavelength decreases from red to violet (about 700 nm for red, 400 nm for violet). So red has the lon... 1
- Ionized hydrogen atoms and α-particles with same momenta enters perpendicular to a constant magnetic field, B. The ratio of their radii of their paths r_H : r_α will be : Answer: 1. 2 : 1 In a magnetic field a charged particle moves in a circle of radius r=p/qB . Momentum p and B are the same, so r∝ 1/q . Ioni... 1
- In a double slit experiment, when light of wavelength 400 nm was used, the angular width of the first minima formed on a screen placed 1 m away, was found to be 0.2^°. What will be the angular width of the first minima, if the entire experimental app… Answer: 2. 0.15^° For the first minimum, sinθ=λ/d . The angle is small, so θ∝λ . In water, λ'=λ/μ=3/4λ . θ'=3/4×0.2^°=0.15^° . 1
- When a block of mass M is suspended by a long wire of length L, the length of the wire becomes (L+l). The elastic potential energy stored in the extended wire is : Answer: 3. 1/2Mgl The energy stored in a stretched wire equals the work done by the stretching force, which grows linearly from 0 to Mg . U=... 1
- A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of 2.5×10^-2 N/m. The pressure inside the bubble equals at a point Z_0 below the free surface of water in a container. Taking g = 10 m/s^2, density of w… Answer: 3. 1 cm A soap bubble has two surfaces, so the excess pressure inside is Δ P=4T/R . Δ P=dfrac4×2.5×10⁻²10⁻³=100\ Pa . At depth Z₀ in... 1
- A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its centre of mass has speed of 20 cm/s. How much work is needed to stop it ? Answer: 1. 3 J To stop the disc we must remove its total kinetic energy, which is translational plus rotational. K=1/2mv²+1/2Iω² with I=1/2m... 1
- Body A of mass 4m moving with speed u collides with another body B of mass 2m, at rest. The collision is head on and elastic in nature. After the collision the fraction of energy lost by the colliding body A is : Answer: 2. 8/9 Use the formula for the final speed of a body in a head-on elastic collision with a body at rest. v_A=m₁-m₂/m₁+m₂u=4m-2m/4m+2... 1
- A mass m is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when : Answer: 3. the mass is at the lowest point The wire breaks where its tension is largest. At the lowest point: T-mg=mv²/r , so T=mg+mv²/r . H... 1
- The kinetic energies of a planet in an elliptical orbit about the Sun, at positions A, B and C are K_A, K_B and K_C, respectively. AC is the major axis and SB is perpendicular to AC at the position of the Sun S as shown in the figure. Then Answer: 3. K_A>K_B>K_C By conservation of angular momentum (Kepler's second law), a planet moves faster when it is closer to the Sun, so its... 1