Gravitation practice · Medium

A system consists of ${N}$ identical particles of mass ${m}$ placed rigidly on the vertices of a regular polygon with each side of length $\ell$. If ${K}_1$ be the kinetic energy imparted to one of the particles so that it just escapes the gravitational pull of the system and there after kinetic energy ${K}_2$ is given by to the adjacent particle to escape, then the difference $\left({K}_1-{K}_2\right)$ is

Assertion: On decreasing the distance between two masses potential energy increases.
Reason: Potential energy $U=\frac{G M m}{r}$.

Choose the incorrect statement from the following:

Self potential energy of a thin uniform shell of mass 2 kg and radius 10 cm is

Given mass of the moon is $1 / 81$ of the mass of the earth and corresponding radius is $1 / 4$ of the earth. If escape velocity on the earth surface is $11.2 {~km} / {s}$, the value of same on the surface of the moon is

A particle is projected vertically upward from the surface of the earth with a speed of $\sqrt{\frac{3}{2} g R}, R$ being the radius of the earth and $g$ is the acceleration due to gravity on the surface of the earth. Then the maximum height ascended is (neglect cosmic dust resistance)

Assertion: The gravitational field of moon is much less than that of earth.
Reason: Gravitational field of a given mass $(M)$ depends upon ${M} / {r}^2$, which is smaller for moon.

A body placed at a distance $R_0$ from the centre of earth, starts moving from rest. The velocity of the body on reaching at the earth's surface will be $\left(\mathrm{R}_{\mathrm{e}}=\right.$ radius of earth and $\mathrm{M}_{\mathrm{e}}=$ mass of earth)

The ratio of the escape velocity to the orbital velocity of a surface satellite of the earth

Two identical satellite A and B are circulating round the earth at the height of R and 2R respectively. (where R is radius of the earth). The ratio of kinetic energy of A to that of B is

The total energy of a satellite is

The mean distance of a planet from the sun is approximately $\frac{1}{4}$ times that of the earth from the sun. Find the number of years required for the planet to make one revolution about the sun. [years].

The height above the surface of the earth, where acceleration due to gravity is $(1 / 64)$ th of its value at surface of the earth is approximately

Two bodies of masses 10 kg and 20 kg are separated by a distance 5 m. Find the gravitational force attraction between two mass $\left[ {G = 6.67 \times {{10}^{ - 11}}\,N{m^2}/k{g^2}} \right]$ is

A body is projected vertically upwards from the surface of planet of mass $\mathrm{M}$ and radius $\mathrm{R}$ with upward speed $\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}}$. The maximum height attained by body is:

If earth stands still what will be its effect on man's weight

The condition for a uniform spherical mass $m$ of radius $r$ to be a black hole is [G = gravitational constant and g = acceleration due to gravity]

Choose the wrong option.

A chain of 125 links is 1.25 m long and has mass of 2 kg with the ends fastened together. It is set for rotating at 50 $\mathrm{rev}{\mathrm{s}^{ - 1}}$, centripetal force on each links is

If the earth stops rotating, the value of $g$ at the equator

According to Kepler's law of planetary motion, if $T$ represents time period and $r$ is orbital radius, then for two planets these are related as

An iron ball and a wooden ball of the same radius are released from a beight $h$ in vacuum. The time taken by both to reach the ground is. The correct option is:

A mass ' $\mathrm{m}$ ' suspended from a spring stretches it by $5 \mathrm{~cm}$ when on the surface of the earth. The mass is then taken on to a height of $1600 \mathrm{~km}$ above earth's surface and again suspended from the same spring. At this altitude the extension of the spring is (Radius of earth = $6400 \mathrm{~km}$)

Astronaut is in a stable orbit around the earth when he weighs a body of mass 5 kg. What is reading of spring balance?

Gravitational potential of the body of mass $m$ at a height $h$ from surface of earth of radius $R$ is (Take $g=$ acceleration due to gravity at earth's surface).

If the rotational motion of earth about its axis
increases, then the weight of a body on equator
would

A small satellite is in elliptical orbit around Earth as shown. If L denotes the magnitude of its angular momentum and K denotes kinetic energy

A satellite of mass m is circulation around the earth with constant angular velocity. If radius of the orbit is ${R_0}$ and mass of the earth M, the angular momentum about the centre of the earth is

Satellite A and B are revolving around the orbit of earth. The mass of A is 10 times of mass of B.The ratio of time period $\left( {\frac{{{T_A}}}{{{T_B}}}} \right)$ is

Assertion(A): Areal velocity of a planet around sun will become two times, if mass of planet is halved.
Reason(R): Areal velocity $=\frac{L}{2 m}$, where $L$ is angular momentum of planet about centre of sun.