IIT JEE & NEET Question Bank with Solution: Gravitation : Physics

Answers are in BOLD Option name.

Q.1. Choose the wrong statement. The escape velocity of a body for a planet depends upon

A) the mass of body

B) the mass of the planet

C) the average radius of the planet

D) the average density of the planet

Q.2. The acceleration due to gravity g on earth is 9.8 ms $blank to the power of negative 2 end exponent$ . What would the value of g fir a planet whose size is the same as that of earth but the density in twice that of earth?

A) 19.6 ms $blank to the power of negative 2 end exponent$

B) 9.8 ms $blank to the power of negative 2 end exponent$

C) 4.9 ms $blank to the power of negative 2 end exponent$

D) 2.45 ms $blank to the power of negative 2 end exponent$

Explanation-

Volume of earth (V) = $fraction numerator 4 straight pi over denominator 3 end fraction R cubed$ . Therefore, density of earth is $rho equals M over V space o r space M equals V rho equals fraction numerator 4 straight pi over denominator 3 end fraction R cubed rho$

Now $g equals fraction numerator G M over denominator R squared end fraction equals fraction numerator 4 πGρR over denominator 3 end fraction$ . Since R is the same for both planets, if $rho$ is doubled, the value of g is also doubled.

Q.3. A satellite id orbiting the earth in a circular orbit of radius r. Its period of revolution varies as

A) $square root of r$

B) $r$

C) $r to the power of 3 divided by 2 end exponent$

D) $r squared$

Explanation-

The speed the satellite is given by

$v equals square root of fraction numerator G M over denominator r end fraction end root$

Therefore, its period of revolution is

$T equals fraction numerator 2 πr over denominator v end fraction equals fraction numerator 2 straight pi over denominator square root of G M end root end fraction. space r to the power of 3 divided by 2 end exponent$

Q.4. Critical velocity of a satellite is a....

A) Vertical velocity given to a satellite so that its orbit is circular

B) Vertical velocity given to a satellite so that its orbit is elliptical

C) Horizontal velocity given to a satellite so that its orbit is elliptical

D) Horizontal velocity given to a satellite so that its orbit is circular

Explanation-

Critical velocity is the maximum velocity given to the satellite in horizontal direction so that it revolves in circular orbit around the earth

Q.5. A planet has (1/49) times the mass and (1/4) times the radius of the earth. The ratio of the accelerations due to gravity on the surface of the planet and the earth is...

A) 16:49

B) 2:7

C) 4:49

D) 4:7

Explanation-

$g fraction numerator G M over denominator R squared end fraction space space space space therefore g subscript 2 over g subscript 1 equals fraction numerator G M subscript 2 over denominator R subscript 2 squared end fraction cross times fraction numerator R subscript 1 squared over denominator G M subscript 1 end fraction equals M subscript 2 over M subscript 1 cross times R subscript 1 squared over R subscript 2 squared M subscript 2 over M subscript 1 equals 1 over 49 space space space space a n d space R subscript 1 over R subscript 2 equals 4 over 1 g subscript 2 over g subscript 1 equals 1 over 49 cross times open parentheses 4 over 1 close parentheses squared equals 16 over 49$

Q.6. If the lift travels vertically downward with uniform velocity equal to 9.8 m/ s the reading of spring balance for a body of weight W in stationary lift is...

A) W

B) 2 W

C) W/2

D) zero

Explanation-

Motion of the lift either downward or upward with uniform velocity makes no difference in the weight. So reading of spring balance is W.

Q.7. The weight of a body on the surface of the earth is 75 kg. The same at a depth equal to one third of the radius of the earth is...

A) 25 kg

B) 50 kg

C) 125 kg

D) 150 kg

Explanation-

$W equals space w e i g h t space o n space s u r f a c e space equals space m g equals space 75 W subscript 1 equals space w e i g h t space a t space d e p t h space d space equals R over 3 equals m g subscript 1 space space space space space space space space space space space d equals R over 3 comma space W subscript 1 over W equals fraction numerator m g subscript 1 over denominator m g end fraction equals open parentheses 1 minus d over R close parentheses equals 2 over 3 space space space space space space space space space space space space space space W subscript 1 equals 2 over 3 cross times W subscript 1 equals 2 over 3 cross times 75 space k g space equals 50 k g space$

Q.8. The binding energy of a stationary body of mass m at height h from the surface of the earth of mass M and radius R is...

A) mGM/(R + h)

B) - mGM/(R + h)

C) mGM/2(R + h)

D) - mGM/2(R + h)

Explanation-

Total energy of a stationary body at height h is

$E equals negative fraction numerator G M m over denominator R plus h end fraction space S o space B E equals plus fraction numerator G M m over denominator R plus h end fraction$

Q.9. The weight of an object in the coal mine , sea level , at the top of the mountain are $straight W subscript 1 space comma space straight W subscript 2 space and space straight W subscript 3$ respectively , then [Odisha JEE 2008 ]

A) $straight W subscript 1 less than straight W subscript 2 greater than straight W subscript 3$

B) $straight W subscript 1 equals straight W subscript 2 equals straight W subscript 3$

C) $straight W subscript 1 less than straight W subscript 2 less than straight W subscript 3$

D) $straight W subscript 1 greater than straight W subscript 2 greater than straight W subscript 3$

Explanation-

Because value of g decreases when we move either in coal mine or at the top of mountain.

Q.10. The value of g decreases inside the surface of Earth because, [ MP PET 2010 ]

A) A force of upward attraction is applied by the shell of Earth above

B) The shell of Earth above exerts no net force

C) The distance from the center of the Earth decreases

D) The density of the material at the Centre of the Earth is very small

Explanation-

Intensity inside a shell is zero.

IIT JEE & NEET Question Bank with Solution

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Tuesday, August 24, 2021

Gravitation : Physics

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