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Let the tangent to the circle x2 + y2 = 25 at the point R (3, 4)
Let the tangent to the circle x2 + y2 = 25 at the point R (3, 4) meet the x-axis and y-axis at points P and Q, respectively. If r is the radius... View ArticleA transmitting station releases waves of wavelength 960 m. A capacitor of 256 μF is used in the resonant circuit. The self inductance of coil necessary for resonance is _____ × 10–8H.
Answer: 10 At resonance ωr = 1/√(Lc) ∴ 2πf = 1/√(Lc) ∴ 4π2c2/λ2 = 1/Lc... View ArticleA coil of inductance 2 H having negligible resistance is connected to a source of supply whose voltage is given by V = 3t volt. (where t is in second). If the voltage is applied when t = 0, then the energy stored in the coil after 4 s is _______ J.
Answer: 144 L di/dt = ε = 3t L ∫di = 3 ∫t dt Li = 3t2/2 i = 3t2/2L Energy stored in the coil, E = ½ Li2 = ½ L (3t2/2L)2 = ½ × 9t4/4L =... View ArticleA monoatomic gas of mass 4.0 u is kept in an insulated container. Container is moving with a velocity 30 m/s. If container is suddenly stopped then change in temperature of the gas (R=gas constant) is x/3R. Value of x is ______.
Answer: 3600 ΔKE = ΔU ΔU = nCVΔT ½ mv2 = (3/2) nRΔT mv2/3nR = ΔT 4×(30)2/3×1×R... View ArticleCircuit of potentiometer
In the given circuit of potentiometer, the potential difference E across AB (10 m length) is larger than E1 and E2 as well. For key K1 (closed),... View ArticleIn a certain thermodynamic process, the pressure of a gas depends on its volume as kV3. The work done when the temperature changes from 1000 C to 3000 C will be ____ nR, where n denotes number of moles of a gas.
Answer: 50 P = kv3 pv–3 = k x = –3 w = nR(T1 - T2)/(x - 1) = nR(100-300)/(-3 -1) = nR(-200)/-4 = 50nR... View ArticleA small bob tied at one end of a thin string of length 1m is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio 5 : 1. The velocity of the bob at the highest position is ______ m/s. (take g = 10 m/s2)
Answer: 5 By conservation of energy, v2min = V2 – 4gl ....(1) Tmax = mg + mv2/l ....(2) Tmin = mv2min/l - mg ....(3) from equation (1) and... View ArticleThe potential energy (U) of a diatomic molecule is a function dependent on r (interatomic distance) as U= α/r10– β/r5 – 3. Where, a and b are positive constants. The equilibrium distance between two atoms will (2α/β)a/b. Where a =_______
Answer: 1 F = -dU/dr F = -[-10α/r11 + 5β/r6] for equilibrium, F = 0 10α/r11 = 5β/r6 2α/β = r5 r =... View Article512 identical drops of mercury are charged to a potential of 2 V each. The drops are joined to form a single drop. The potential of this drop is ____ V.
Answer: 128 Let charge on each drop = q Radius = r V = kq/r 2 = kq/r Radius of bigger 4πR3/3 = 512 × (4/3) πr3 R = 8r V =... View ArticleThe electric field in a region is given by [latex]left ( frac{3}{5}E_{o}hat{i}+ frac{4}{5}E_{o}hat{j}right )frac{N}{C}[/latex]. The ratio of flux of reported field through the rectangular surface of area 0.2 m2 (parallel to y-z plane) to that of the surface of area 0.3 m2(parallel to x-z plane) is a : 2, where a = ________
[Here i, j and k are unit vectors along x, y and z-axes respectively] Answer: 1 Therefore, a = 1 ... View ArticleThe same size images are formed by a convex lens when the object is placed at 20 cm or at 10 cm from the lens. The focal length of a convex lens is ______ cm.
Answer: 15 1/v – 1/u = 1/f ...(1) m = v/u ....(2) from (1) and (2) we get m = f/(f + u) Given conditions m1 = -m2 f/(f - 10) = -f/(f... View ArticleMagnetic fields at two points on the axis of a circular coil at a distance of 0.05 m and 0.2 m from the centre are in the ratio 8 : 1. The radius of coil is ______
a. 0.15 m b. 0.2 m c. 0.1 m d. 1.0 m Answer: (c) B = μ0NiR2/2(R2 + x2)3/2 at x1 = 0.05m, B1 = μ0NiR2/2(R2 + (0.05)2)3/2 at x2 =... View ArticleTwo coherent light sources having intensities in the ratio 2x produce an interference pattern. The ratio (Imax – Imin)/(Imax + Imin) will be:
a. 2√(2x)/(x + 1)b. √(2x)/(2x + 1)c. 2√(2x)/(2x + 1)d. √(2x)/(x + 1)
a. 2√(2x)/(x + 1) b. √(2x)/(2x + 1) c. 2√(2x)/(2x + 1) d. √(2x)/(x + 1) Answer: (c) Let I1 = 2x I2 = 1 Imax = (√I1... View Article