The gravitational potential energy of a body of mass ‘m’ at the earth’s surface $-mg{R}_{\mathcal{e}}$. Its gravitational potential energy at a height ${R}_{\mathcal{e}}$ from the earth’s surface will be (Here ${R}_{\mathcal{e}}$  is the radius of the earth)

(a)       $-2mg{R}_{\mathcal{e}}$              (b)        $2mg{R}_{\mathcal{e}}$

(c)       $\frac{1}{2}mg{R}_{\mathcal{e}}$               (d)        $-\frac{1}{2}mg{R}_{\mathcal{e}}$

Concept Questions :-

Gravitational potential energy
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Difficulty Level:

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

(a) Doubles                   (b)  Becomes half

(c)  Remains same        (d)   Becomes zero

Concept Questions :-

Acceleration due to gravity
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Difficulty Level:

Escape velocity of a body of 1 kg mass on a planet is 100 m/sec. Gravitational Potential energy of the body at the planet is -

(a)   – 5000 J                      (b)  – 1000 J

(c)   – 2400 J                       (d)  5000 J

Concept Questions :-

Gravitational potential energy
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Difficulty Level:

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 ?

(a)     The mass of the brass ball on this planet is a quarter of its mass as measured on earth

(b)  The weight of the brass ball on this planet is a quarter of the weight as measured on earth

(c)   The brass ball has the same mass on the other planet as on earth

(d)  The brass ball has the same volume on the other planet as on earth

Concept Questions :-

Acceleration due to gravity
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Difficulty Level:

A body of mass m is placed on the earth’s surface. It is taken from the earth’s surface to a height 3R . The change in gravitational potential energy of the body is -

(a)   $\frac{2}{3}mgR$                      (b) $\frac{3}{4}mgR$

(c)    $\frac{mgR}{2}$                       (d) $\frac{mgR}{4}$

Concept Questions :-

Gravitational potential energy
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Difficulty Level:

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

(a) $1.99×{10}^{30}kg$                        (b) $7.56×{10}^{22}kg$

(c) $5.98×{10}^{24}kg$                       (d) $7.65×{10}^{22}kg$

Concept Questions :-

Acceleration due to gravity
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Difficulty Level:

A geo-stationary satellite is orbiting the earth at a height of 6 R above the surface of earth, R being the radius of earth. The time period of another satellite at a height of 2.5 R from the surface of earth is

(a) 10 hr                          (b)

(c) 6 hr                            (d)

Concept Questions :-

Kepler laws
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Difficulty Level:

A body of mass m kg starts falling from a point 2R above the Earth’s surface. Its kinetic energy when it has fallen to a point ‘R’ above the Earth’s surface [- Radius of Earth, - Mass of Earth, G - Gravitational Constant] -

(a)        $\frac{1}{2}\frac{GMm}{R}$               (b) $\frac{1}{6}\frac{GMm}{R}$

(c)        $\frac{2}{3}\frac{GMm}{R}$               (d) $\frac{1}{3}\frac{GMm}{R}$

Concept Questions :-

Gravitational potential energy
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Difficulty Level:

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

(a)  g decreases by 2% and K decreases by 4%

(b)  g decreases by 4% and K increases by 2%

(c)  g increases by 4% and K increases by 4%

(d)  g decreases by 4% and K increases by 4%

Concept Questions :-

Acceleration due to gravity
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Difficulty Level:

The distance between centre of the earth and moon is 384000 km. If the mass of the earth is  and  . The speed of the moon is nearly -

(a) 1 km/sec                          (b) 4 km/sec

(c) 8 km/sec                          (d) 11.2 km/sec

Concept Questions :-

Orbital velocity