Q. No.Starting from the centre of the earth, having radius \(R,\) the variation of \(g\) (acceleration due to gravity) is shown by:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
| 1. | \(\dfrac R {n^2}\) | 2. | \(\dfrac {R~(n-1)} n\) |
| 3. | \(\dfrac {Rn} { (n-1)}\) | 4. | \(\dfrac R n\) |
Radii and densities of two planets are \(R_1, R_2\) and \(\rho_1, \rho_2\) respectively. The ratio of accelerations due to gravity on their surfaces is:
1. \(\frac{\rho_1}{R_1}:\frac{\rho_2}{R_2}\)
2. \(\frac{\rho_1}{R^2_1}: \frac{\rho_2}{R^2_2}\)
3. \(\rho_1 R_1 : \rho_2R_2\)
4. \(\frac{1}{\rho_1R_1}:\frac{1}{\rho_2R_2}\)
\(1\) kg of sugar has maximum weight:
1. at the pole.
2. at the equator.
3. at a latitude of \(45^{\circ}.\)
4. in India.
| 1. | \(g' = 3g\) | 2. | \(g' = 9g\) |
| 3. | \(g' = \frac{g}{9}\) | 4. | \(g' = 27g\) |
| Assertion (A): | Generally the path of a projectile from the Earth is parabolic but it is elliptical for a projectile going to a very great height. |
| Reason (R): | At the ordinary height, the projectile moves under a uniform gravitational force, but for great heights, the projectile moves under a variable force. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
| 1. | \(32\) N | 2. | \(56\) N |
| 3. | \(72\) N | 4. | zero |
A body weighs \(200\) N on the surface of the earth. How much will it weigh halfway down the centre of the earth?
| 1. | \(100\) N | 2. | \(150\) N |
| 3. | \(200\) N | 4. | \(250\) N |
The density of a newly discovered planet is twice that of Earth. If the acceleration due to gravity on its surface is the same as that on Earth, and the radius of Earth is \(R,\) what will be the radius of the new planet?
| 1. | \(4R\) | 2. | \(\dfrac{1}{4}R\) |
| 3. | \(\dfrac{1}{2}R\) | 4. | \(2R\) |
The height of a point vertically above the earth’s surface, at which the acceleration due to gravity becomes \(1\%\) of its value at the surface is: (Radius of the earth = \(R\))
1. \(8R\)
2. \(9R\)
3. \(10R\)
4. \(20R\)
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