Q. No.If the acceleration due to gravity experienced by a point mass at a height \(h\) above the surface of the earth is the same as that of the acceleration due to gravity at a depth \(\alpha h\left(h \ll \mathrm{R}_e\right)\) from the earth's surface. The value of \(\alpha\) will be:
(use \(R_e = 6400~\text{km}\))
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)
(use \(R_e = 6400~\text{km}\))
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)
Subtopic: Acceleration due to Gravity |
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Two girls are standing on the edge of a building tossing coins over the edge. Alice is dropping her coins, each of which is \(10~\text{gm}.\) Barbara is tossing her coins horizontally at \(0.3~\text{m/s},\) and her coins are \(40~\text{gm}\) each (see figure). Ignore air resistance.
When the coins are in free fall, acceleration of one of Alice’s coins compared to the acceleration of one of Barbara’s coins is:
| 1. | One-fourth |
| 2. | Same |
| 3. | Four times |
| 4. | Dependent on the height at which the acceleration is recorded |
Subtopic: Acceleration due to Gravity |
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The weight of an object on the earth’s surface is \(400\) N. What would be the weight of the same object at a depth \(\dfrac{R}{2}\) from the surface?
(where \(R\) is the radius of the earth)
(where \(R\) is the radius of the earth)
| 1. | \(100\) N | 2. | \(300\) N |
| 3. | \(200\) N | 4. | \(250\) N |
Subtopic: Acceleration due to Gravity |
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The height from the surface of the earth at which the value of \(g\) becomes one-fourth of that on the earth’s surface will be:
(\(R\) is the radius of the earth)
| 1. | \(2.45 R\) | 2. | \(1.45 R\) |
| 3. | \(R\) | 4. | \(\dfrac{5}{6}R\) |
Subtopic: Acceleration due to Gravity |
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If the diameter of the earth becomes half keeping mass constant, then the acceleration due to gravity at the surface of the earth becomes:
| 1. | half | 2. | four times |
| 3. | twice | 4. | three times |
Subtopic: Acceleration due to Gravity |
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A \(\mathrm{DNA}\) sample has a mass of \(2~\text{mg},\) and an \(\mathrm{RNA}\) sample has a mass three times that of the \(\mathrm{DNA}.\) What is the ratio of the weight of the \(\mathrm{DNA}\) to the weight of the \(\mathrm{RNA}\) if both were weighed on the Moon?
| 1. | \(1: 29.4\) | 2. | \(1:6\) |
| 3. | \(1: 4.9\) | 4. | \(1: 3\) |
Subtopic: Acceleration due to Gravity |
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What is the ratio of acceleration due to gravity at an altitude \(h=R\) to the value at the surface of the earth? (where \(𝑅\)=radius of earth)
1. \(1:2\)
2. \(1:4\)
3. \(1:8\)
4. \(1:6\)
1. \(1:2\)
2. \(1:4\)
3. \(1:8\)
4. \(1:6\)
Subtopic: Acceleration due to Gravity |
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When a body of weight \(72\text{ N}\) moves from the surface of the Earth at a height half of the radius of the earth, then the gravitational force exerted on it will be:
1. \(36\text{ N}\)
2. \(32\text{ N}\)
3. \(144\text{ N}\)
4. \(50\text{ N}\)
Subtopic: Acceleration due to Gravity |
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The percentage decrease in the weight of a rocket, when it is taken to a height of \(32~\text{km}\) above the surface of the Earth will be:
(radius of the Earth \(R=6400~\text{km} \))
(radius of the Earth \(R=6400~\text{km} \))
| 1. | \(1\text{%}\) | 2. | \(3\text{%}\) |
| 3. | \(4\text{%}\) | 4. | \(0.5\text{%}\) |
Subtopic: Acceleration due to Gravity |
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At what height \(h\) above the Earth does the value of \(g\) become \(\dfrac{g}{2}?\) (where \(R\) is the radius of the Earth)
| 1. | \(3R\) | 2. | \(\sqrt{2}R\) |
| 3. | \(\left({\sqrt{2}-1}\right){R}\) | 4. | \(\dfrac{1}{\sqrt{2}}R\) |
Subtopic: Acceleration due to Gravity |
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