Gravitational Field

Q. The maximum vertical distance through which a full dressed astronaut can jump on the Earth is $0.5\text{m}$. The maximum vertical distance through which astronaut can jump on the Moon, which has a mean density ${\left(\frac{2}{3}\right)}^{rd}$ that of the earth and radius one quarter that of the earth is (in $m$)

Q.

Three particles each of mass m, are situated at the vertices of an equilateral triangle of side length a. The only forces acting on the particles are their mutual gravitational forces. It is desired that each particle moves in a circle while maintaining the original separation a. Find the initial velocity that should be given to each particle and also the time required for the circular motion

1. 

2. 

3. 

4. 

Q.

The figure shows a uniform spherical shell of mass M. The point A is not at the centre but away from the centre of the shell. If a particle of mass m is placed at A, then

1. It remains at rest

2. It experiences a net force towards the centre

3. It experiences a net force away from centre

4. None of the above

Q.

The figure represents a solid uniform sphere of mass M and radius R. A spherical cavity of radius r is at a distance a from the centre of the sphere. The gravitational field inside the cavity is

1. Towards the centre of the cavity

2. Non- uniform

3. Directly proportional to a

4. All of the above

Q.

Three particles A, B and C, each of mass m, are placed in a line with AB = BC = d. Find the gravitational force on a fourth particle P of same mass, placed at a distance d from the particle B on the perpendicular bisector of the line AC.

1. 

2. 

3. 

4. 

Q.

The distance of the centres of moon and earth is D. The mass of earth is 81 times the mass of the moon.
At what distance from the centre of the earth, the gravitational force will be zero

1. 

2. 

3. 

4. 

Q.

Gravitational field at the centre of semicircle formed by a thin wire AB of mass m and length l is

1. $\frac{GM}{{\pi l}^2}$ along y - axis

2. $\frac{2\pi GM}{l^2}$

3. $\frac{GM}{l^2}$ along x - axis

4. $\frac{2\pi GM}{l^2}$

Q.

Two particles of equal mass go round a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is--

1. 

2. 

3. 

4. 

Q.

Force of gravity is least at

1. The equator

2. A point in between equator and any pole

3. The poles

4. None of these

Q.

If there were a smaller gravitational effect, which of the following forces do you think would alter in some respect

1. Archimedes uplift

2. Electrostatic force

3. None of the above

4. Viscous forces