Q. No.Two spherical bodies of masses M and 5M and radii R and 2R are released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before the collision is:
1. 2.5 R
2. 4.5 R
3. 7.5 R
4. 1.5 R
A mass M is split into two parts, m and (M–m), which are then separated by a certain distance. What ratio of m/M maximizes the gravitational force between the two parts
1. 1/3
2. 1/2
3. 1/4
4. 1/5
The height at which the weight of a body becomes 1/16th of its weight on the surface of the earth (radius R) is:
1. 5 R
2. 15 R
3. 3 R
4. 4 R
A mass M is split into two parts, m and (M–m), which are then separated by a certain distance. What ratio of m/M maximizes the gravitational force between the two parts
1. 1/3
2. 1/2
3. 1/4
4. 1/5
The figure shows two concentric shells of masses m, and m. At which point a particle of mass m shall experience zero gravitational force because of them?
(1) A
(2) C
(3) D
(4) B
Kepler's third law states that the square of the period of revolution (T) of a planet around the sun, is proportional to the third power of the average distance r between the sun and planet i.e. T2=Kr3, here K is constant. If the masses of the sun and planet are M and m respectively, then as per Newton's law of gravitation, the force of attraction between them is F=GMm/r2, here G is gravitational constant. The relation between G and K is described as
1. GK=4π2
2. GMK=4π2
3. K=G
4. K=l/G
| 1. | \( \dfrac{2}{9}{F} \) | 2. | \(\dfrac{16}{9} F\) |
| 3. | \(\dfrac{8}{9} F\) | 4. | \(F\) |
| 1. | occurs only when the objects have very different masses |
| 2. | is greater on the more massive of the two objects |
| 3. | is not an attractive force |
| 4. | increases in magnitude as the two objects approach each other |
| Column-I | Column-II | ||
| (A) | Force on any particle (units of \(Gm^2/a^2\)) |
(I) | \(3\) |
| (B) | Potential energy of the system (units of \(-Gm^2/a\)) |
(II) | \(\sqrt3\) |
| (C) | Gravitational potential due to any particle at the centre \((O)\) (units of \(-Gm/a\)) |
(III) | \(\dfrac43\) |
| (D) | Gravitational field at the mid-point of a side (units of \(Gm/a^2\)) |
(IV) | \(\dfrac23\) |
| 1. | A-I, B-II, C-IV, D-III |
| 2. | A-III, B-I, C-I, D-II |
| 3. | A-II, B-I, C-II, D-III |
| 4. | A-I, B-III, C-IV, D-II |
| 1. | \({\dfrac{2Gm^2}{a^2}}\) | 2. | \({\dfrac{Gm^2}{a^2}}\) |
| 3. | \({\dfrac{\sqrt3}{2}\dfrac{Gm^2}{a^2}}\) | 4. | \({\dfrac{\sqrt3Gm^2}{a^2}}\) |
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