Gravitation practice · Mixed difficulty

The acceleration due to gravity on a planet is same as that on earth and its radius is 16 times that of earth. What will be the value of escape velocity on that planet if it is ${V_e}$ on earth.

A clock S is based on oscillation of a spring and a clock P is based on pendulum motion. Both clocks run at the same rate on earth. On a planet having the same density as earth but twice the radius

Time period of revolution of a nearest satellite around a planet of radius $R$ is $T$. Period of revolution around another planet, whose radius is $4 R$ but having same density is

The acceleration due to gravity is $g$ at a point distant $r$ from the centre of earth of radius $R$. If $r < R$, then

The gravitational field at some point in space is $\overrightarrow g = 8\hat i + 6\hat j\,N/kg$. The force exerted on a 1 kg mass placed at that point is

If mass of a satellite is doubled and time period remain constant the ratio of orbit in the two cases will be

The correct option is

A uniform spherical shell gradually shrink maintaining its shape. The gravitational potential at its centre will (Mass of the shell remains same)

A body is projected vertically upwards from the surface of the earth with a speed equal to $\frac{1}{4}$th of escape velocity from surface of earth. Maximum height attained by the body from the surface of the earth will be ($R$-Radius of earth)

The angular speed with which earth should spin about its axis, such that a person feels $\left(\frac{5}{9}\right)^{\text {th}}$ times his weight at equator as compared to his weight at pole

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

Which of the following statement is correct? (Take, earth as a sphere of uniform density)

When you move from equator to pole, the value of acceleration due to gravity ( $\mathrm{g}$ )

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.