Physics - Gravitation - Quiz-6

The mass of a planet that has a moon whose time period and orbital radius are T and R respectively can be written as -

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$4 π^{2} R^{3} G^{‐ 1} T^{‐ 2}$
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$8 π^{2} R^{3} G^{‐ 1} T^{‐ 2}$
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$12 π^{2} R^{3} G^{‐ 1} T^{‐ 2}$
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$16 π^{2} R^{3} G^{‐ 1} T^{‐ 2}$

The eccentricity of earth's orbit is 0.0167. The ratio of its maximum speed in its orbit to its minimum speed is

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() 2.507
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() 1.033
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() 8.324
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() 1.000

Assuming the earth to have a constant density, point out which of the following curves show the variation of acceleration due to gravity from the centre of earth to the points far away from the surface of earth -

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1
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2
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3
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4

The radius of orbit of a planet is two times that of the earth. The time period of the planet is:

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4.2 years
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2.8 years
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5.6 years
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8.4 years

The diagram showing the variation of gravitational potential of earth with distance r from the centre of earth is -

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1
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2
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3
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4

The orbital angular momentum of a satellite revolving at a distance r from the centre is L. If the distance is increased to 16r, then the new angular momentum will be -

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16 L
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64 L
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$\frac{L}{4}$
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4L

The condition for a uniform spherical mass m of radius r to be a black hole is [G= gravitational constant and g= acceleration due to gravity] .

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${(2 G m / r)}^{1 / 2} \leq c$
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${(2 G m / r)}^{1 / 2} = c$
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${(2 G m / r)}^{1 / 2} \geq c$
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${(g m / r)}^{1 / 2} \geq c$

A sphere of mass M and radius R₂ has a concentric cavity of radius R₁ as shown in figure. The force F exerted by the sphere on a particle of mass m located at a distance r from the centre of sphere varies as $(0 \leq r \leq \infty)$ .

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1
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2
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3
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4

Which one of the following graphs represents correctly the variation of the gravitational field (I) with the distance (r) from the centre of a spherical shell of mass M and radius a ?

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1
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2
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3
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4

Suppose, the acceleration due to gravity at the earth’s surface is 10 $m / s^{2}$ and at the surface of Mars, it is 4.0 $m / s^{2}$ . A 60 kg passenger goes from the earth to Mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky. Which part of the figure best represents the weight (net gravitational force) of the passenger as a function of time ?

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() D
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() B
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() C
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() A

Which of the following graphs represents the motion of a planet moving about the sun ?

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1
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2
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3
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4

The correct graph representing the variation of total energy ( $E_{t}$ ), kinetic energy ( $E_{k}$ ) and potential energy (U) of a satellite with its distance from the centre of the earth is -

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1
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2
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3
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4

What is the intensity of gravitational field of the centre of a spherical shell?

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$G m / r^{2}$
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g
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Zero
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None of these

The diameters of two planets are in the ratio 4 : 1 and their mean densities in the ratio 1 : 2. The acceleration due to gravity on the planets will be in the ratio of:

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1 : 2
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2 : 3
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2 : 1
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4 : 1

If the angular speed of the earth is doubled, the value of acceleration due to gravity (g) at the north pole

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Doubles
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Becomes half
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Remains same
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Becomes zero

At the surface of a certain planet, acceleration due to gravity is one-quarter of that on earth. If a brass ball is transported to this planet, then which one of the following statements is not correct?

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The mass of the brass ball on this planet is a quarter of its mass as measured on earth
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The weight of the brass ball on this planet is a quarter of the weight as measured on earth
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The brass ball has the same mass on the other planet as on earth
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The brass ball has the same volume on the other planet as on earth

Weight of 1 kg becomes 1/6 kg on moon. If radius of moon is $1.768 \times 10^{6} m$ , then the mass of moon will be -

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(a) $1.99 \times 10^{30} k g$
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(b) $7.56 \times 10^{22} k g$
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(c) $5.98 \times 10^{24} k g$
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(d) $7.65 \times 10^{22} k g$

Let g be the acceleration due to gravity at earth's surface and K be the rotational kinetic energy of the earth. Suppose the earth's radius decreases by 2% keeping all other quantities same, then

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g decreases by 2% and K decreases by 4%
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g decreases by 4% and K increases by 2%
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g increases by 4% and K increases by 4%
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g decreases by 4% and K increases by 4%

The distance between centre of the earth and moon is 384000 km. If the mass of the earth is $6 \times 10^{24} k g$ and $G = 6.66 \times 10^{- 11} N m^{2} / k g^{2}$ . The speed of the moon is nearly -

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() 1 km/sec
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() 4 km/sec
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() 8 km/sec
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() 11.2 km/sec

A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is -

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R/3
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R/2
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R/4
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R/5

A satellite is launched into a circular orbit of radius R around the Earth while a second satellite is launched into an orbit of radius 1.02R. The percentage difference in the time periods of the two satellites is

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0.7
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1.0
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1.5
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3

Distance of geostationary satellite from the center of the Earth $(R_{e} = 6400 k m)$ in terms of $R_{e}$ is-

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$13.76 R_{e}$
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$10.76 R_{e}$
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$6.59 R_{e}$
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$2.56 R_{e}$

Energy required to move a body of mass m from an orbit of radius 2R to 3R is

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$G M m / 12 R^{2}$
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$G M m / 3 R^{2}$
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$G M m / 8 R$
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$G M m / 6 R$

If the radius of the earth contracts by 2% and its mass remains the same, then weight of the body at the earth surface :

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Will decrease
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Will increase
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Will remain the same
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None of these

The kinetic energy needed to project a body of mass m from the earth surface (radius R) to infinity is -

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mgR/2
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2 mgR
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mgR
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mgR/4

A satellite is to revolve round the earth in a circle of radius 8000 km. The speed at which this satellite be projected into an orbit, will be

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$3 k m / s$
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16 km/s
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7.15 km/s
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8 km/s

If the mass of a body is M on the earth surface, then the mass of the same body on the moon surface is:

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M/6
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Zero
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M
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None of these

Radius of orbit of satellite of earth is R. Its kinetic energy is proportional to -

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$\frac{1}{R}$
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$\frac{1}{\sqrt{R}}$
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R
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$\frac{1}{R^{3 / 2}}$

A particle falls towards earth from infinity. It’s velocity on reaching the earth would be -

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Infinity
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$\sqrt{2 g R}$
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$2 \sqrt{g R}$
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Zero

Two satellite A and B, ratio of masses 3 : 1 are in circular orbits of radii r and 4r. Then ratio of total mechanical energy of A to B is

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1 : 3
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3 : 1
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3 : 4
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12 : 1

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Practice Physics Quiz Questions and Answers

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Practice Physics Quiz Questions and Answers

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