1

Two equal masses separated by a distance '$d$' attract each other with a force '$F$'. If one unit of mass is transferred from one of them to the other, the force:

If the mass of one particle is increased by 50 % and the mass of another particle is decreased by 50 %, the gravitational force between them

The point at which the gravitational force acting on any mass is zero due to the Earth and the Moon system is (The mass of the Earth is approximately $81$ times the mass of the Moon and the distance between the Earth and the Moon is $3,85,000km$.)

Two stationary particles of masses $M_{1}$ and $M_{2}$ are at distance d apart. A third particle, lying on the line joining the particles, experiences no resultant gravitational force. The distance of this particle from $M_{1}$ is

A solid sphere of uniform density and radius $R$ applies a gravitational force of attraction equal to $F_{1}$ on a particle placed at a distance 3R from the centre of the sphere. A spherical cavity of radius $2R $ is now made in the sphere, as shown in the figure. The sphere with cavity now applies a gravitational force $F_{2}$ on the same particle. The ratio $F_{1}F_{2} $ is

In a hypothetical case, if the diameter of the earth becomes half of its present value and its mass becomes four times of its present value, then how would the weight of any object on the surface of the earth be affected?

If $g$ on the surface of the Earth is $9.8ms_{−2}$, its value at a height of $6400km$ is: (Radius of the Earth $=6400km$)

A point $P$ is on the axis of a fixed ring of mass $M$ and radius $R$, at a distance $2R$ from the centre $O$. A small particle starts from $P$ and reaches $O$ under the gravitational attraction only. Its speed at $O$ will be

The gravitational potential difference between the surface of a planet and a point $20$m above it is $16$ J/kg. Calculate the work done in moving a $4$kg body by $8$m on a slope of $60_{o}$ from the horizontal.

The Jupiter's period of revolution around the Sun is $12$ times that of the Earth. Assuming the planetary orbits to be circular, find how many times the distance between the Jupiter and the Sun exceeds that between the Earth and the Sun.

Two satellites are revolving round the earth at different heights. The ratio of their orbital speeds is $2:1$. If one of them is at a height of $100km$, the height of the other satellite is $($Radius of earth $R=6400$ km $)$