Home
Class 11
PHYSICS
It is known that the time of revolution ...

It is known that the time of revolution T of a satellite around the earth depends on the universal gravitational constant G, the mass of the earth M, the radius of the circular orbit R. Obtain an expression for T using dimensional analysis.

Text Solution

Verified by Experts

We have `" "[T] prop [G]^(a)[M]^(b)[R]^(c )`
`rArr [M]^(a)[L]^(0)[T]^(1)= [M]^(-a)[L]^(3a)[T]^(-2a) xx [M]^(b)xx [L]^(c ) = [M]^(b-a) [L](c+3a) [T]^(-2a)`
Comparing the exponents
For [T]: `1= -2a rArr a = - (1)/(2)" "` For [M]: `0=b-a rArr b-a= - (1)/(2)`
For [L]: `0= c+3a rArr c= -3a = (3)/(2)`
Putting the values we get `T prop G^(-1//2) M ^(-1//2) R ^(3//2) rArr T prop sqrt((R^(3))/(GM))`
The actual expression is T `= 2pi sqrt((R^(3))/(GM))`
Promotional Banner

Topper's Solved these Questions

  • PHYSICAL WORLD, UNITS AND DIMENSIONS & ERRORS IN MEASUREMENT

    ALLEN |Exercise BEGINNER S BOX-1|2 Videos

  • PHYSICAL WORLD, UNITS AND DIMENSIONS & ERRORS IN MEASUREMENT

    ALLEN |Exercise BEGINNER S BOX-2|4 Videos

  • MISCELLANEOUS

    ALLEN |Exercise Question|1 Videos

  • SEMICONDUCTORS

    ALLEN |Exercise Part-3(Exercise-4)|50 Videos

Similar Questions

Explore conceptually related problems

It is known that the time of revolution T of a satellite around the earth depends on the universal gravitational constant G, the mass of the earth M, and the radius of the circular orbit R. Obtain an expression for T using dimensional analysis.

Length of a year on a planet is the duration in which it completes one revolution around the sun. Assume path of the planet known as orbit to be circular with sun at the centre. The length T of a year of a planet orbiting around the sun in circular orbit depends on universal gravitational constant G, mass m_(s) of the sun and radius r of the orbit. if TpropG^(a)m_(s)^(b)r^(c) find value of a+b+2c.

Obtain an equation of orbital time period of satellite revolves around the earth.

A satellite moves around the earth in a circular orbit with speed v . If m is the mass of the satellite, its total energy is

An artificial satellite is revolving around a planet of mass M and radius R in a circular orbit of radius r. From Kepler's third law about the period of a satellite around a common central body, square of the period of revolution T is proportional to the cube of the radius of the orbit r. Show using dimensional analysis that T=(k)/(R) sqrt((r^(3))/(g)) where k is dimensionless RV g constant and g is acceleration due to gravity.

A satellite of mass m goes round the earth along a circular path of radius r. Let m_(E) be the mass of the earth and R_(E) its radius then the linear speed of the satellite depends on.

An artificial satellite revolves around the earth, remaining close to the surface of the earth, Show that its time period is T = 2pi sqrt(R_e/g)

If the mass of earth is M, radius R and G is universal gravitational constant then the workdone against gravity to move a body of mass 1 kg from the surface of earth to infinity will be

The distance moved by a particle in time from centre of ring under the influence of its gravity is given by x=a sin omegat where a and omega are constants. If omega is found to depend on the radius of the ring (r), its mass (m) and universal gravitation constant (G), find using dimensional analysis an expression for omega in terms of r, m and G.

The minimum and maximum distances of a satellite from the centre of the earth are 2R and 4R respectively where R is the radius of earth and M is the mass of the earth find radius of curvature at the point of minimum distance.