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A 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 Article

The 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 Article

512 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 Article

The 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 Article

The 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 Article

Magnetic 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 Article

Two coherent light sources having intensities in the ratio 2x produce an interference pattern. The ratio (I_max – I_min)/(I_max + I_min) 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

The angular frequency of alternating current in a L-C-R circuit is 100 rad/s. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.

The angular frequency of alternating current in a L-C-R circuit is 100 rad/s. The components connected are shown in the figure. Find the value of... View Article

Given below are two statements: one is labelled as Assertion A and the other is labelled as reason R

Assertion A: The escape velocities of planet A and B are same. But A and B are of unequal masses. Reason R: The product of their masses and radii... View Article

An α particle and a proton are accelerated from rest by a potential difference of 200 V. After this, their de Broglie wavelengths are λ_α and λ_p respectively. The ratio λ_p/λ_α is:

a. 8 b. 2.8 c. 3.8 d. 7.8 Answer: (b) λ = h/p = h/√(2mqV) λp/λα = √(mαqα/mpqp) =... View Article

If the time period of a two meter long simple pendulum is 2 s, the acceleration due to gravity at the place where pendulum is executing S.H.M. is:

a. 2π2 ms–2 b. 16 m/s2 c. 9.8 ms–2 d. π2 ms–2 Answer: (a) T = 2π√(l/g) T2 = 4π2l/g g = 4π2l/T2 =... View Article

The pitch of the screw gauge is 1 mm and there are 100 divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lines 8 divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while 72^nd division on circular scale coincides with the reference line. The radius of the wire is

a. 1.64 mm b. 1.80 mm c. 0.82 mm d. 0.90 mm Answer: (c) Least count. = pitch/no. of div. = 1 mm/100 = 0.01 mm +ve zero error = 8 × L.C. =... View Article

Match List-I with List-II:

Match List-I with List-II: List-I List-II (a)h (Planck’s constant) (i) [MLT–1] (b)E... View Article

Two radioactive substances X and Y originally have N₁ and N₂ nuclei respectively. Half-life of X is half of the half-life of Y. After three half-lives of Y, numbers of nuclei of both are equal. The ratio N₁/N₂ will be equal to:

Two radioactive substances X and Y originally have N1 and N2 nuclei respectively. Half-life of X is half of the half-life of Y. After... View Article

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: When a rod lying freely is heated, no thermal stress is developed in it. Reason R: On heating, the length of the rod increases In the light of the above statements, choose the correct answer from the options given below:

a. A is true but R is false b. Both A and R are true and R is the correct explanation of A c. Both A and R are true but R is NOT the correct... View Article

A proton, a deuteron and an α particle are moving with the same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is _ and their speeds are in the ratio.

A proton, a deuteron and an α particle are moving with the same momentum in a uniform magnetic field. The ratio of magnetic forces acting... View Article

An engine of a train, moving with uniform acceleration, passes the signal post with velocity u and the last compartment with velocity v. The velocity with which middle point of the train passes the signal post is:

a. √(v2 - u2)/2 b. (v - u)/2 c. √(v2 + u2)/2 d. (u + v)/2 Answer: (c) a = uniform acceleration u = velocity of first compartment v =... View Article

Two satellites A and B of masses 200 kg and 400 kg are revolving round the earth at height of 600 km and 1600 km respectively. If TA and TB are the time periods of A and B respectively then the value of TB – TA:

Two satellites A and B of masses 200 kg and 400 kg are revolving round the earth at height of 600 km and 1600 km respectively. If TA and TB are... View Article

The current (i) at time t = 0 and t = ∞ respectively for the given circuit is:

The current (i) at time t = 0 and t = ∞ respectively for the given circuit is: a. 18E/55,5E/18 b. 5E/18,18E/55 c. 5E/18,10E/33... View Article

NISHTHA Scheme

The National Initiative for School Heads' and Teachers' Holistic Advancement (NISHTHA) is a capacity building programme for “Improving Quality of... View Article

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