Physics MCQs for NEET — Practice Questions with Answers

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The mean radius of the earth is R, its angular speed on its own axis is ω and the acceleration due to gravity at earth's surface is g. The cube of the radius of the orbit of a geostationary satellite will be -

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Explanation

(d)   Orbital velocity vo=GMr=gR2r and vo=rω

        This gives r3=R2gω2

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A satellite whose mass is M, is revolving in circular orbit of radius r around the earth. Time of revolution of satellite is

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Explanation

(b)T=2πrv  ...(1)and mv2r=GmeMr2⇒v2=Gmeror, v=Gmer  ...(2)

Putting the value of v from equation (2) in equation (1) 

T=2πrGmer=2πr3Gme⇒T α r3GMe

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The periodic time of a communication satellite is

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Explanation

(d) Communication satellite is a kind  of geostationary satellite so its time period is  24 hours.

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Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to -

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Explanation

(a) mω2R∝ 1Rn⇒m4π2T2R∝ 1Rn⇒T2∝ Rn+1∴T∝ Rn+12

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The orbital speed of an artificial satellite very close to the surface of the earth is Vo. Then the orbital speed of another artificial satellite at a height equal to three times the radius of the earth is 

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Explanation

(c)     v∝1r, If r=R then v=V0

          If r=R+h=R+3R=4R  then v=Vo2=0.5 V0

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 If the radius of the earth were to shrink by 1% its mass remaining the same, the acceleration due to gravity on the earth's surface would -

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Explanation

(c) g=GMR2; If mass remains constant then g∝ 1r2

 % increase in g = 2(% decrease in R) = 2x1% = 2%

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The distance of a geo-stationary satellite from the centre of the earth (Radius R = 6400 km) is nearest to -

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Explanation

(b)    6R from the surface of earth and 7R from the centre.

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In order to make the effective acceleration due to gravity equal to zero at the equator, the angular velocity of rotation of the earth about its axis should be (g=10 ms-2 and radius of earth is 6400 kms)

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Explanation

(b)  g'=g-ω2Rcos2λ 

For weightlessness at equator λ=0 and g'=0

∴0=g-ω2R⇒ω=gR=1800rads

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 A simple pendulum has a time period T1 when on the earth’s surface and T2 when taken to a height R above the earth’s surface, where R is the radius of the earth. The value of is T2/T1 is 

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Explanation

(d) If acceleration due to gravity is g at the surface of earth then at height R its value becomes g'=gRR+h2=g4

T1=2πlg  and T2=2πlg/4  

∴T2T1=2

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A body of mass m is taken from earth surface to the height h equal to radius of earth, the increase in potential energy will be

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Explanation

(b) ∆U=mgh1+hR=12mgR (∵h=R)

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