Gravitation - Mechanics - Physics Previous Year Questions

A rocket is fired vertically with a speed of $4 \mathrm{~km} / \mathrm{s}$ from the earth's surface. How far from the earth does the rocket go before returning to the earth?

(Take, radius of earth $=6.4 \times 10^6 \mathrm{~m}$ and $g=10 \mathrm{~m} / \mathrm{s}^2$ )

Three particles, each of mass $M$, situated at the vertices of an equilateral triangle of side length $l$. 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 $l$. The initial speed that should be given to each particle is

The ratio of orbital velocity of a body near to the surface of a planet and escape velocity of a body from the surface of the same planet is

Gravitational forces operate among which of the following?

The percentage increase in the energy for an artificial satellite to shift it from an orbit of radius $r$ to an orbit of radius $3 r / 2$ is

A body of mass $m$ is at height $R$ from the surface of the earth where $R$ is the radius of the earth. If the body is taken from here to a height of $3 R$ from the surface of the earth, the increase in the gravitational potential energy of the body is

( $g$ is acceleration due to gravity on the surface of the earth)

The graph correctly represents the variation of acceleration due to gravity $(g)$ with radial distance from the centre of the earth (radius of the earth $=R_e$ ) is

Choose the correct statement.

Four particles each of mass $m$ are placed at four vertices of a rectangle having side length as $3 l_0$ and $4 l_0$. The potential energy of the system in $\frac{G m^2}{l_0}$ is

A uniform sphere $A$ with radius $R$ exerts a force $F$ on a small particle $B$ situated at a distance $2 R$ from the centre of the sphere. A spherical portion of diameter $R$ is cut from the sphere $A$ as shown in the figure. If $F^{\prime}$ is the new gravitational force between the remaining part of the sphere $A$ and the particle $B$, then the correct relation between $F$ and $F^{\prime}$

Statement I The force of attraction due to a hollow spherical shell of uniform density on a point mass situated inside it is always positive.

Statement II The force of attraction between a hollow spherical shell of uniform density and a point mass situated outside is same just as, if the entire mass of the shell is at the centre of the shell.

Which of the following is correct?

Let the escape speed of an object on the earth's surface be $v_0$. The object is projected out with speed $5 v_0$. The speed of the object far away from the earth will be

If the radius of the earth shrinks by $1 \%$, its mass remaining the same, then the acceleration due to gravity on the earth surface would

The long range force experienced by a neutral particle with a finite mass

A planet is moving in an elliptical orbit around the sun. The work done on the planet by the gravitational force of the sun

(i) is zero in no part of the motion.

(ii) is zero in some parts of the orbit.

(iii) is zero in one complete revolution.

(iv) is zero in any small part of the orbit.

Which of the following is true?

If the escape velocity on earth is $11.2 \mathrm{~km} / \mathrm{s}$, its value for a planet having double the radius and 8 time the mass of earth is

A mass $M$ is split into two parts $m_0$ and $M-m_0$. These two masses are then separated by a distance $D$. If the gravitational force between the parts is maximum, then the ratio $\frac{m_0}{M}$ is