Physics

Assertion A: If A, B, C, D are four points on a semi-circular arc with centre at 'O' such that |AB| = |BC| = |CD|, then AB + AC + AD = 4AO + OB + OC
Reason R: Polygon law of vector addition yields AB + BC + CD = AD = 2AO

In the light of the above statements, choose the most appropriate answer from the options given below:

The relative permittivity of distilled water is 81. The velocity of light in it will be: (Given µ? = 1)

A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of cross-sectional area 'a' is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is (a << A):

A particle of mass 4M at rest disintegrates into two particles of mass M and 3M respectively having non zero velocities. The ratio of de-Broglie wavelength of particle of mass M to that of mass 3M will be :

In the reported figure, a capacitor is formed by placing a compound dielectric between the plates of parallel plate capacitor. The expression for the capacity of the said capacitor will be: (Given area of plate = A)

Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are m, 2m and 2m respectively. A moves towards B with a speed of 9m/s and makes an elastic collision with it. Thereafter B makes a completely inelastic collision with C. All motions occur along same straight line. The final speed of C is:

The half-life of ¹?Au is 3 days. If atomic weight of ¹?Au is 198 g/mol then the activity of 2 mg of ¹?Au is [ in disintegration / second ] :

A capacitor of capacitance C = 1µF is suddenly connected to a battery of 100 volt through a resistance R = 100Ω. The time taken for the capacitor to be charged to get 50 V is: [Take ln 2 = 0.69]

A parallel plate capacitor with plate area 'A' and distance of separation 'd' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as

ε(x) = ε? + kx, for 0 < x d/2
ε(x) = ε? + k(d-x), for d/2 ≤ x ≤ d

In the given figure, a battery of emf E is connected across a conductor PQ of length 'l' and different area of cross- sections by having radii r? and r? (r? < r?). Choose the correct option as one moves from P to Q: