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Q. No.

The mass of a planet is \(\left ( \dfrac{1}{10} \right )^{{th}}\) that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is: 
1. \(9.8 ~\text{ms}^{-2}\) 2. \(4.9 ~\text{ms}^{-2}\)
3. \(3.92 ~\text{ms}^{-2}\) 4. \(19.6~\text{ms}^{-2}\)
Q1:
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Subtopic:  Acceleration due to Gravity |
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The minimum energy required to launch a satellite of mass \(m\) from the surface of earth of mass \(M\) and radius \(R\) in a circular orbit at an altitude of \(2R\) from the surface of the earth is:
1. \(\dfrac{2 G m M}{3 R} \)
2. \(\dfrac{G m M}{2 R} \)
3. \(\dfrac{G m M}{3 R} \)
4. \( \dfrac{5 G m M}{6 R}\)
Q2:
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Subtopic:  Satellite |
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A rocket is fired vertically upward with a speed of \(\dfrac{v_e}{\sqrt2}\) from the earth's surface, where \(v_e\) is escape velocity on the surface of earth. The distance from the surface of earth upto which the rocket can go before returning to the earth is
(Given radius of earth \(=6400~\text{km}\) ) :
1. \(1600~\text{km}\)
2. \(3200~\text{km}\)
3. \(6400~\text{km}\)
4. \(12800~\text{km}\)
Q3:
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Subtopic:  Escape velocity |
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A body weighing \(100~\text{N}\) on the surface of earth weights \(x~\text{kg-ms}^{-2}\) at a height \(\frac{1}{9} R_E\) above the surface of earth.
The value of \(x\) (\(g= 10~\text{ms}^{-2}\) at surface of earth and \(R_E\) is the radius of earth): 
1. \(72\) 
2. \(54\)
3. \(81\) 
4. \(62\)
Q4:
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Subtopic:  Acceleration due to Gravity |
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Two bodies of mass \(m\) and \(9m\) are placed at a distance \(R\). The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be: (\(G\) = gravitational constant)
1. \(-\dfrac{20~GM}{R}\)
2. \(-\dfrac{8~GM}{R}\)
3. \(-\dfrac{12~GM}{R}\)
4. \(-\dfrac{16~GM}{R}\)
Q5:
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Subtopic:  Gravitational Potential |
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A satellite is orbiting just above the surface of the earth with period \(T.\) If \(d\) is the density of the earth and \(G\) is the universal constant of gravitation, the quantity \(\frac{3 \pi}{G d}\) represents:
1. \(\sqrt{T}\)
2. \(T\)
3. \(T^2\)
4. \(T^3\)
Q6:
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Subtopic:  Satellite |
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The escape velocity of a body on the earth's surface is \(11.2\) km/s. If the same body is projected upward with a velocity \(22.4\) km/s, the velocity of this body at infinite distance from the center of the earth will be:
1. \(11.2\sqrt2\) km/s 2. zero
3. \(11.2\) km/s 4. \(11.2\sqrt3\) km/s
Q7:
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Subtopic:  Escape velocity |
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If \(R\) is the radius of the earth and \(g\) is the acceleration due to gravity on the earth surface. Then the mean density of the earth will be:
1. \(\dfrac{\pi RG}{12g}\) 2. \(\dfrac{3\pi R}{4gG}\)
3. \(\dfrac{3g}{4\pi RG}\) 4. \(\dfrac{4\pi G}{3gR}\)
Q8:
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Subtopic:  Acceleration due to Gravity |
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A body of mass \(60~ \text{g}\)  experiences a gravitational force of \(3.0~\text{N}\) when placed at a particular point. The magnitude of the gravitational field intensity at that point is:
1. \(180 ~\text{N/kg}\) 2. \(0.05 ~\text{N/kg}\)
3. \(50 ~\text{N/kg}\) 4. \(20 ~\text{N/kg}\)
Q9:
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Subtopic:  Gravitational Field |
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Assuming the earth to be a sphere of uniform density, its acceleration due to gravity acting on a body:

1. increases with increasing altitude.
2. increases with increasing depth.
3. is independent of the mass of the earth.
4. is independent of the mass of the body.
Q10:
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Subtopic:  Acceleration due to Gravity |
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