Gravity and Gravitation | Numerical Solution

[2076 'C']

A remote sensing satellite of the earth revolves in a circular orbit at a height of $250$ km above the earth's surface. What is the orbital speed and period of revolution of the satellite?

[2075 'A']

A man can jump $1.5\;m$ on earth. Calculate the approximate height he might be able to jump on a planet whose density is one-quarter of the earth and where the radius is one third that of the earth. [Click here for Solution]

[Ans: $18 \; m$]

[2075 'B']

An artificial satellite revolves around the earth in $2.5 \; hours$ in a circular orbit. Find the height of the satellite above the earth assuming earth as a sphere of radius $6370  \; km$. [Click here for Solution]

[Ans: $3.03 \;*\; 10^6\;m$]

[2074 'Supp.']

Obtain the value of $'g'$ from the motion of moon assuming that its period of rotation around the earth is $27$ days $8$ hours and the radius of its orbit is $60.1$ times the radius of the earth. [Click here for Solution]

[Ans: $9.8\;m/s^2$]

[2074 'A']

The period of the moon revolving under the gravitational force of the earth is $27.3$ days. Find the distance of the moon from the center of the earth if the mass of the earth is $5.97 \;*\;10^{24}kg$. [Click here for Solution]

[Ans: $3.98\;*\;10^8\;m$]

[2073 'C']

Mass of earth is nearly $81$ times heavier than the moon. Its diameter is about $4$ times larger than that of the moon. Estimate the value of the acceleration of gravity on the surface of the moon. [Click here for Solution]

[Ans: $1.975\;m/s^2$]

[2073 'D']

Taking the earth to be the uniform sphere of radius $6400 \; km$, calculate the total energy needed to raise a satellite of mass $1000 \; kg$ to a height of $600 \; km$ above the ground and to set it into a circular orbit at that altitude. [Click here for Solution]

[Ans: $3.4\;*\;10^{10}\;J$]

[2072 'C']

Taking the earth to be the uniform sphere of radius $6400 \; km$ and the value of $g$ at the surface to be $10\;m/s^2$, calculate the total energy needed to raise a satellite of mass $2000 \; kg$ to a height of $800 \; km$ above the ground and to set it into a circular orbit at that altitude. [Click here for Solution]

[Ans: $7.12\;*\;10^{10}\;J$]

[2071 'D']

An earth satellite moves in a circular orbit with a speed of $6.2\;km/s$. Find the time of one revolution and its centripetal acceleration. [Click here for Solution]

[Ans: $175$ min, $3.7$ m/s$^2$]

[2071 'D']

Calculate the points along a line joining the centers of earth and moon where there is no gravitational force. ($M_e = 6 * 10^{24}\;kg, M_m = 7.4 * 10^{22}\;kg, d = 3.8 * 10^8\;m$). [Click here for Solution]

[2066]

What is the period of revolution of a satellite of mass m that orbits the earth in a circular path of radius $7880 \; km$ about $1500 \; km$ above the surface of the earth? [Click here for Solution]

[Ans: $1.93$ hrs]

[2062]

How far away from the surface of the earth does the acceleration due to gravity becomes $4$ % of its value on the surface of the earth? Take the radius of the earth as $6400 \; km$. [Click here for Solution]

[Ans: $25.6\;*\;10^6\;m$]

[2054]

Calculate the period of revolution of a satellite revolving at a distance of $20 \; km$ above the surface of the earth, (Radius of the earth = $6400 \; km$. Acceleration due to gravity = $10 \; m/s^2$). [Click here for Solution]

[Ans: $5050.13 \; sec$]

[2051]

A $200 \; kg$. satellite is lifted to an orbit of $2.2\;*\;10^4\;km$ radius. If the radius and mass of the earth are $6.37\;*\;10^6\;m$. and $5.98\;*\;10^{24};kg$ respectively, how much additional potential energy is required to lift the satellite? [Click here for Solution]

[Ans: $4.47\;*\;10^7\;J$]