Suppose the gravitational force varies inversely as the $n^{th}$ power of distance. Then the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to
Suppose the gravitational force varies inversely as the $n^{th}$ power of distance. Then the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to
- A
${R^{\left( {\frac{{n + 1}}{2}} \right)}}$
- B
${R^{\left( {\frac{{n - 1}}{2}} \right)}}$
- C
${R^n}$
- D
${R^{\left( {\frac{{n - 2}}{2}} \right)}}$
Similar Questions
$Assertion$ : The escape speed does not depend on the direction in which the projectile is fired.
$Reason$ : Attaining the escape speed is easier if a projectile is fired in the direction the launch site is moving as the earth rotates about its axis.
$Assertion$ : The escape speed does not depend on the direction in which the projectile is fired.
$Reason$ : Attaining the escape speed is easier if a projectile is fired in the direction the launch site is moving as the earth rotates about its axis.
A body of mass $m$ is situated at distance $4R_e$ above the Earth's surface, where $R_e$ is the radius of Earth how much minimum energy be given to the body so that it may escape
A body of mass $m$ is situated at distance $4R_e$ above the Earth's surface, where $R_e$ is the radius of Earth how much minimum energy be given to the body so that it may escape
A skylab of mass $m\,kg$ is first launched from the surface of the earth in a circular orbit of radius $2R$ (from the centre of the earth) and then it is shifted from this circular orbit to another circular orbit of radius $3R$ . The minimum energy required to shift the lab from first orbit to the second orbit are
A skylab of mass $m\,kg$ is first launched from the surface of the earth in a circular orbit of radius $2R$ (from the centre of the earth) and then it is shifted from this circular orbit to another circular orbit of radius $3R$ . The minimum energy required to shift the lab from first orbit to the second orbit are
The change in the value of $g$ at a height $h$ above the surface of the earth is the same as at a depth $d$ below the surface of earth. When both $d$ and $h$ are much smaller than the radius of earth, then which one of the following is correct ?
The change in the value of $g$ at a height $h$ above the surface of the earth is the same as at a depth $d$ below the surface of earth. When both $d$ and $h$ are much smaller than the radius of earth, then which one of the following is correct ?
In order to make the effective acceleration due to gravity equal to zero at the equator, the angular velocity of rotation of the earth about its axis should be $(g = 10\,m{s^{ - 2}}$ and radius of earth is $6400 \,kms)$
In order to make the effective acceleration due to gravity equal to zero at the equator, the angular velocity of rotation of the earth about its axis should be $(g = 10\,m{s^{ - 2}}$ and radius of earth is $6400 \,kms)$