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In a cylinder a heavy piston is moving with speed v as shown diagram and gas is filled inside it. A gas molecule is moving with speed v₀ towards moving piston. Then which of the following is correct. (Assume v <<<< v₀ Δl/l ) and collision is elastic)

a) change in speed after collision is 2V b) change is speed after collision is 2 v0 Δl/l c) rate of collision is V/l d) When piston is at... View Article

A free hydrogen atom after absorbing a photon of wavelength λ_a gets excited from state n = 1 to n = 4. Immediately after electron jumps to n = m state by emitting a photon of wavelength λ_e. Let change in momentum of atom due to the absorption and the emission are ΔP_a and Δp_e respectively. If λ_a/ λ_e= 1/5. Which of the following is correct

a) m = 2 b) ΔPa/Pe = 1/2 c) λe = 418 nm d) Ratio of K.E. of electron in the state n = m to n = 1 is ¼. Answer: a::d... View Article

A dipole of Dipole moment [latex]p = frac{p_0}{sqrt 2}(hat i + hat j)[/latex] is placed at origin. Now a uniform external electric field at magnitude E₀ is applied along direction of dipole. Two points A and B are lying on a equipotential surface of radius R centered at origin. A is along axial position of dipole and B is along equatorial position. There correct option are:

a) Net electric field at point A is 3E0 b) Net electric field at point B is Zero c) Radius of equatorial surface R = (kp0/E0)1/3 d) Radius... View Article

The given arrangement is released from rest when spring is in natural length. Maximum extension in spring during the motion is x₀, a₁, a₂ and a₃ are accelerations of the blocks.

Make the correct options a) a2 – a1 = a1 – a3 b) x0 = 4mg/3k c) d) Acceleration a1 at x0/4 is 3kx0/42m Answer: a::c::d 2a1 = a2 +... View Article

Monoatomic gas A having 5 mole is mixed with diatomic gas B having 1 mole in container of volume V0. Now the volume of mixture is compressed to V0/4 by adiabatic process. Initial pressure and temperature of gas mixture is P₀ and T₀. [given 2^3.2 = 9.2] Choose correct option:

a) b) Final pressure is between 9P0 and 10P0 c) |W.D.| = 13 RT0 d) Average Translational kinetic energy Answer: a::b::c W = [P1V1 –... View Article

A uniform rigid rod of mass m & length l is released from vertical position on rough surface with sufficient friction for lower end not to slip as shown in figure. When rod makes angle 60° with vertical then find correct alternatives

a) b) c) N = mg/16 d) aradical = 3g/4 Answer: b::c::d mg – N = mav N = mg/16... View Article

In YDSE monochromatic light of wavelength 600 nm incident of slits as shown in figure.

If S1S2 = 3mm, OP = 11 mm then a) If α = 0.36/π degree then destructive interfaces at point P. b) If α = 0.36/π degree then constructive... View Article

Consider two plane convex lens of same radius of curvature and refractive index n₁ and n₂ respectively. Now consider two cases:

Case – I: When n1 = n2 = n, then equivalent focal length of lens is f0. Case – II: When n1 = n, n2 = n + Δn, then equivalent focal length of... View Article

An optical bench, to measure the focal length of lens, is 1.5 m long and on the bench marks are with spacing 1/4 cm. Now a lens is placed at 75 cm and pin type object is placed at 45 cm marks on the bench. If its image is formed at 135 cm find maximum possible error in calculation of focal length.

Answer: df/f = 1.38 and 1.39 V = 30 cm and dv = 0.5 cm V = 60 cm and dv = 0.5 cm Now, using lens formula, 1/v - 1/u = 1/f 1/60 + 1/30 = 1/f... View Article

A weight of 100 N is suspended by two wires made by steel and copper as shown in figure length of steel wire is 1 m and copper wire is √3 m. Find ratio of change in length of copper wire (Δ l₀) to change in length of steel wire (Δ l_s). Given Young’s modulus: Y_steel= 2 × 10¹¹ N/m², Y_copper = 1 × 10¹¹ N/m².

Answer: 2... View Article

The source S₁ is at rest. The observer and the source S₂ are moving towards S₁ as shown in figure. The roof beats observed by the observer if both sources have frequency 120 Hz and speed of sound 330 m/s in is

Answer: 8.128Hz... View Article

If at angle θ the light takes maximum time to travel in optical fiber. Then the maximum time is x (10^-8), calculate x.

Answer: 10 1.5 sin θC = 1.44 sin 900 sin θC = 24/25 and sin θC = x/d ⇒ d = 25x/24 Now, t = L/(C/n2) = 5 x 10-8s Putting: C = 3... View Article

N dielectrics are introduced in series in a capacitor of thickness D. Each dielectric have width d = D/N & dielectric constant of mth dielectric is given by K_m = K(1 + m/N) : [N >> 10³, Area of plates = A]. Net capacitance is given by [KЄ_oA]/[αDln2]. Find value of α.

Answer: 1x/m = Δ/N Integrating we get Ceq = [KЄoA]/[Dln2] Therefore, α = 1... View Article

Consider the following nuclear fission reaction

In this fission reaction. Kinetic energy of α-particle emitted is 4.44 MeV. Find the energy emitted as γ – radiation in keV in this reaction.... View Article

Apparent depth for point object x in all three cases are H1, H2 & H3 respectively when seen from below given H = 30 cm, n = 1.5 & R = 3m, then

a) 0.8 < H2 - H1 < 0.9 b) H2 > H1 c) H2 > H3 d) H3 > H1 Answer: Case 1: ⇒ 1/n = d1/(3Q) ⇒ d1 = (30/3) x 2 =... View Article

V – T diagram for n mol monoatomic gas is given below:

c) Work done in cyclic process is ΔW = nRT0/2 d) There are only adiabatic and isochoric processes are involved Answer: (a) and (b)... View Article

If in a hypothetical system if the angular momentum and mass are dimensionless. Then which of the following is true.

a) The linear momentum varies as L-1 b) The energy varies as L-2 c) The power varies as L-4 d) The force varies as L-5 Answer: (a), (b) and... View Article

Conducting wire of parabolic shape, initially y = x² is moving with velocity [latex]\vec v = v_0 \hat i[/latex] in a non-uniform magnetic field [latex]\vec B = B_0(1 + (y/L)^{\beta}) \hat k[/latex] as shown in figure. If V0, B0, L and B are +ve constants and Δϕ is potential difference develop between the ends of wire, then correct statement(s) is/are

a) |Δφ| = (1/2) B0V0L for β = 0 b) |Δφ| = (4/3) B0V0L for β = 2 c) |Δφ| is proportional to the length of wire projected on y-axis. d) |Δφ|... View Article

A galvanometer of resistance 10 ohm and maximum current of 2μA is converted into voltmeter of range 100 mV and when converted into ammeter then range is 1mA. When these voltmeter and ammeter are connected by a (ideal) battery in series with a resistance of R = 1000 Ω, then

a) Measured value of R is between 978Ω and 996Ω b) Resistance of voltmeter 105Ω c) Shunt resistance is 20mΩ d) If the ideal battery is... View Article

choose the right options

a) At time t = 0, the S1 is closed instantaneous current in the closed circuit will be 25 mA b) The key S1 is kept closed for long time such... View Article