Physics
- A screw gauge gives the following readings when used to measure the diameter of a wireMain scale reading : 0 mmCircular scale reading : 52 divisionsGiven that 1 mm on main scale corresponds to 100 divisions on the circular scale. The diameter of the… Answer: 4. 0.052 cm Key idea: diameter = main scale reading + circular reading × least count. Least count =1\ mm/100=0.01 mm. Diameter =0+52... 1
- The escape velocity from the Earth's surface is v. The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is : Answer: 4. 4v Key idea: v_e=√(2GM/R) and M=4/3π R³ρ , so v_e∝ Rsqrtρ . Same density and radius four times as large gives v_e'=4v . Option 4. 1
- A car starts from rest and accelerates at 5 m/s^2. At t = 4 s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t = 6 s ? (Take g = 10 m/s^2) Answer: 4. 20√(2) m/s, 10 m/s ² Key idea: once the ball is dropped, its horizontal velocity stays equal to the car's velocity at that instan... 1
- A small block slides down on a smooth inclined plane, starting from rest at time t = 0. Let S_n be the distance travelled by the block in the interval t = n − 1 to t = n. Then, the ratio S_nS_n+1 is : Answer: 2. 2n-1/2n+1 Key idea: distance in the n-th second from rest is S_n=1/2a(2n-1) . S_n∝(2n-1) and S_(n+1)∝(2n+1) , so dfracS_nS_(n+1)=... 1
- A thick current carrying cable of radius 'R' carries current 'I' uniformly distributed across its cross-section. The variation of magnetic field B(r) due to the cable with the distance 'r' from the axis of the cable is represented by : Answer: 3. Graph (3): B vs r, linear rise to a peak then decreasing Key idea: use Ampere's law inside and outside the cable. Inside ( r Outs... 1
- A uniform conducting wire of length 12a and resistance 'R' is wound up as a current carrying coil in the shape of,(i) an equilateral triangle of side 'a'.(ii) a square of side 'a'.The magnetic dipole moments of the coil in each case respectively are… Answer: 1. √(3) Ia² and 3 Ia² Key idea: magnetic moment M=NIA , where N is the number of turns the wire of length 12a gives. Triangle (side... 1
- In the productF = q(v×B) = q v×(Bi+Bj+B_0k)For q = 1 and v = 2i+4j+6k and F = 4i-20j+12kWhat will be the complete expression for B ? Answer: 2. -6i-6j-8k Key idea: expand vec v×vec B as a determinant and match components. Here vec v=(2,4,6) , vec B=(B_x,B_y,B_z) , vec F=(4... 1
- A point object is placed at a distance of 60 cm from a convex lens of focal length 30 cm. If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of 40 cm from it, the final image would be formed at a distance of… Answer: 4. 20 cm from the plane mirror, it would be a virtual image. Key idea: lens, then mirror, then lens again. Lens: u=-60,\ f=30⇒ v=60... 1
- If E and G respectively denote energy and gravitational constant, then E/G has the dimensions of : Answer: 1. [M²][L⁻¹][T⁰] Key idea: get the dimensions of G from F=Gm₁m₂/r² . [G]=M⁻¹L³T⁻² and [E]=ML²T⁻² . E/G=dfracML²T⁻²M⁻¹L³T⁻²=M²L⁻¹T⁰ .... 1
- A uniform rod of length 200 cm and mass 500 g is balanced on a wedge placed at 40 cm mark. A mass of 2 kg is suspended from the rod at 20 cm and another unknown mass 'm' is suspended from the rod at 160 cm mark as shown in the figure. Find the value… Answer: 4. 1/12 kg Key idea: take torques about the wedge (40 cm mark). The rod's weight acts at its centre (100 cm). Anticlockwise (left):... 1
- Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of the input energy. How much power is generated by the turbine ? (g = 10 m/s^2) Answer: 2. 8.1 kW Key idea: power input = (mass per second) × g × h; the turbine gets 90% of it. P_in=15×10×60=9000\ mathrm W P_out=0.9×9000... 1
- Column - I gives certain physical terms associated with flow of current through a metallic conductor. Column - II gives some mathematical relations involving electrical quantities. Match Column - I and Column - II with appropriate relations.Column -… Answer: 1. (A)-(R), (B)-(S), (C)-(P), (D)-(Q) (A) Drift velocity v_d=aτ=eE/mτ : R. (B) Resistivity ρ=E/J : S. (C) From ρ=m/ne²τ , relaxation... 1
- A capacitor of capacitance 'C', is connected across an ac source of voltage V, given byV = V_0 ω tThe displacement current between the plates of the capacitor, would then be given by : Answer: 1. I_d = V₀ω Ccosω t Key idea: displacement current equals the conduction current that charges the capacitor. q = CV = CV₀sinω t I_d... 1
- For a plane electromagnetic wave propagating in x-direction, which one of the following combination gives the correct possible directions for electric field (E) and magnetic field (B) respectively ? Answer: 2. -j+k,\ -j-k Key idea: vec E , vec B and the direction of propagation are mutually perpendicular, and vec E×vec B points along pro... 1
- Consider the following statements (A) and (B) and identify the correct answer.(A) A zener diode is connected in reverse bias, when used as a voltage regulator.(B) The potential barrier of p-n junction lies between 0.1 V to 0.3 V. Answer: 3. (A) is correct and (B) is incorrect. Key idea: a Zener diode regulates voltage only in reverse-bias breakdown, and the barrier po... 1
- The equivalent capacitance of the combination shown in the figure is : Answer: 2. 2C Key idea: wires joining the two sides short-circuit a capacitor, and the rest become parallel. The right-hand vertical wire jo... 1
- A dipole is placed in an electric field as shown. In which direction will it move ? Answer: 2. towards the right as its potential energy will decrease. Key idea: in a non-uniform field a dipole feels a net force towards the... 1
- A parallel plate capacitor has a uniform electric field 'E' in the space between the plates. If the distance between the plates is 'd' and the area of each plate is 'A', the energy stored in the capacitor is : (ε_0 = permittivity of free space) Answer: 3. 1/2ε₀E²Ad Key idea: energy density in an electric field is 1/2ε₀E² ; multiply by the volume between the plates. U=1/2ε₀E²× Ad . O... 1
- Match Column - I and Column - II and choose the correct match from the given choices.Column - I: (A) Root mean square speed of gas molecules; (B) Pressure exerted by ideal gas; (C) Average kinetic energy of a molecule; (D) Total internal energy of 1… Answer: 3. (A) - (Q), (B) - (P), (C) - (S), (D) - (R) (A) rms speed =√(3RT/M) matches Q. (B) Pressure =1/3 nmbar v² matches P. (C) Average k... 1
- An infinitely long straight conductor carries a current of 5 A as shown. An electron is moving with a speed of 10^5 m/s parallel to the conductor. The perpendicular distance between the electron and the conductor is 20 cm at an instant. Calculate the… Answer: 4. 8×10⁻²⁰ N Key idea: the electron moves parallel to the wire, so vec v⊥vec B and F=evB . B=μ₀I/2π r=dfrac2×10⁻⁷×50.2=5×10⁻⁶\ mathr... 1
- A convex lens 'A' of focal length 20 cm and a concave lens 'B' of focal length 5 cm are kept along the same axis with a distance 'd' between them. If a parallel beam of light falling on 'A' leaves 'B' as a parallel beam, then the distance 'd' in cm w… Answer: 2. 15 Key idea: a parallel beam stays parallel only if the lens separation makes the focal points coincide. The convex lens A focuse... 1
- A lens of large focal length and large aperture is best suited as an objective of an astronomical telescope since : Answer: 4. all of the above. Key idea: for a telescope objective, large focal length gives larger magnification, and large aperture helps th... 1
- A body is executing simple harmonic motion with frequency 'n', the frequency of its potential energy is : Answer: 2. 2n Key idea: potential energy depends on x² , so it repeats twice per oscillation. x = Asinω t ⇒ U=1/2 kx²=1/2 kA²sin²ω t=1/4 kA²... 1
- Find the value of the angle of emergence from the prism. Refractive index of the glass is √(3). Answer: 1. 60^° Key idea: a ray hitting a face along its normal goes straight in; then apply Snell's law at the next face. The ray enters th... 1