Physics MCQs for NEET — Practice Questions with Answers

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The masses and radii of the earth and moon are M1, R1 and M2, R2 respectively. Their centres are distance d apart. The minimum velocity with which a particle of mass m should be projected from a point midway between their centres so that it escapes to infinity is

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Explanation

(a) Gravitational potential at mid point

     V=-GM1d/2+-GM2d/2Now,  PE=m×V=-2GMdM1+M2[m = mass of particle]So, for projecting particle from mid point to infinity

     KE=PE12mv2=2 GmdM1+M2v=2GM1+M2d

If mass of earth is M, radius is R and gravitational constant is G, then work done to take 1 kg mass from earth surface to infinity will be

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Explanation

(b) Potential energy of the 1 kg mass which is placed at the earth surface=-GMR

     its potential energy at infinite = 0

     Work done = change in potential energy =GMR

If ve and vo represent the escape velocity and orbital velocity of a satellite corresponding to a circular orbit of radius R, then 

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Explanation

(b)   ve=2gR and vo=gR 2vo=ve

If r represents the radius of the orbit of a satellite of mass m moving around a planet of mass M, the velocity of the satellite is given by: 

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Explanation

Fe=mv2r and Fg=GMmr2

For the satellite to revolve in the orbit the centripetol force must be blamed  by gravitational force i.e.

FC=Fgmv2r=GMmr2v2=GMr

An earth satellite of mass m revolves in a circular orbit at a height h from the surface of the earth. R is the radius of the earth and g is acceleration due to gravity at the surface of the earth. The velocity of the satellite in the orbit is given by

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Explanation

(d)    vo=GMr=gR2R+h

A satellite which is geostationary in a particular orbit is taken to another orbit. Its distance from the centre of earth in new orbit is 2 times that of the earlier orbit. The time period in the second orbit is 

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Explanation

(b)     Tr3/2. If r becomes double then time period will becomes 232 times.
          So new time period will be 24×22 hr i.e. T=482

The ratio of the K.E. required to be given to the satellite to escape earth's gravitational field to the K.E. required to be given so that the satellite moves in a circular orbit just above earth atmosphere is 

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Explanation

(b)        K.E. required for satellite to escape from earth's gravitational field

            12mve2=12m2GMR2=GMmR

             K.E. required for satellite to move in circular orbit

             12mvo2=12mGMR2=GMm2R

            The ratio between these two energies = 2

An astronaut orbiting the earth in a circular orbit 120 km above the surface of earth, gently drops a spoon out of space-ship. The spoon will

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Explanation

(c)          The velocity of the spoon will be equal to the orbital velocity when dropped

               out of the space-ship.

The period of a satellite in a circular orbit around a planet is independent of 

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Explanation

(c) Time period of earth satellite

T=2πR3GM

so, it is independent of mass of satellite.

Two identical satellites A and B go round a planet P in circular orbits having radii 4R and R respectively. If the speed of the satellite A is 3V, the speed of the satellite B will be ?

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Explanation

(b)               v=GMRvAvB=RBRA=R4R=12vAvB=3VvB=12 vB=6V

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