Plz answer these
1. Define Period of conical pendulum and obtain expression for it's time period
2.critical vel of satellite and obtain its expression
3.state Kepler's law of planetary motion
4.explain refraction of light on the for basis of wave theory.prove laws of refraction
5.condition for constructive and destructive interference of light
Answers
Answer:
Q.1 Consider a conical pendulum with a bob of mass m, length l, at an angle θ with the vertical, going round with a uniform velocity v and radius r, as shown in the figure.
The forces acting on the mass are the tension on the string T′, and the force of gravity mg.
The vertical component of the tension balances the force of gravity and the horizontal component provides the centripetal force to keep the bob in uniform circular motion.
⇒T′cosθ=mg and T′sinθ=mv2r.
⇒gcosθ=T′m=v2rsinθ⇒gcosθ=v2rsinθ.
⇒v2=rgtanθ⇒v=rgtanθ−−−−−−√.
The period of a conical pendulum is the time taken to go round the circular path once.
⇒ The period, T=2πrv=2πrrgtanθ√=2πrgtanθ−−−−−√.
It can be seen that r=lsinθ.
⇒T=2πlsinθgtanθ−−−−−√=2πlcosθg−−−−√.
⇒ The period of a conical pendulum is 2πlcosθg−−−−√.
Q.2 Critical Velocity of Satellite. The constant horizontal velocity given to the satellite so as to put it into stable circular orbit around the earth is called as critical velocity and is denoted by Vc. It is also known as orbital speed or proper speed.
Q 3 Kepler’s three laws of planetary motion can be stated as follows: (1) All planets move about the Sun in elliptical orbits, having the Sun as one of the foci. (2) A radius vector joining any planet to the Sun sweeps out equal areas in equal lengths of time. (3) The squares of the sidereal periods (of revolution) of the planets are directly proportional to the cubes of their mean distances from the Sun.
Q 4 Laws of refraction
Ratio of velocity of light in rarer medium to velocity of light in denser medium is a constant called refractive index of denser medium w.r.t. rarer medium. The incident rays, refracted rays and normal lie in the same plane. Incident ray and refracted ray lie on opposite sides of normal.
Explanation:Phenomenon of refraction can be explained on the basis of wave theory of light.
Let XY be the plane refracting surface separating two media air and glass of respectively. indices μ1 and μ2 refractive.A plane wave front AB is advancing obliquely towards XY from air. It is bounded by rays AA1 and BB1 which are incident rays.When ‘A’ reaches ‘A1’, then ‘B’ will be at ‘P’. It still has to cover distance PB1 to reach XY.
According to Huygens’ principle, secondary wavelets will originate from A1 and will spread over a hemisphere in glass.All the rays between AA1 and BB1 will reach XY and spread over the hemispheres of increasing radii in glass.
The surface of tangency of all such hemispheres is RB1.
This gives rise to refracted wave front B1R in glass.A1R and B1R1 are refracted rays.
Let c1 and c2 be the velocities of light in air and glass respectively..
At any instant of time ‘t’,
distance covered by incident wavefront
from P to B1 = PB1 = c1t
Distance covered by secondary wave from A1 to R = A1R = c2t.
hope you got it
Q 5 To set up a stable and clear interference pattern, two conditions must be met: The sources of the waves must be coherent, which means they emit identical waves with a constant phase difference. The waves should be monochromatic - they should be of a single wavelength.