An infinite number of masses each of one kg

Asked by admin @ 20/08/2021 in Physics viewed by 333 People

Infinite number of masses, each of 1 kg, are placed along the x-axis at x = +- 1m, +- 2m, +-4m, +- 8m, +- 16m.. The gravitational of the resultant gravitational potential in term of gravitaitonal constant G at the origin (x = 0) is

Answered by admin @ 20/08/2021

Given :

Mass of each body = 1 kg

Masses are placed along X-axis at x = +- 1m , +- 2m , +-4m, +-8m ,+-16m ......

To Find :

The resultant of gravitational potential of all the masses in terms of gravitational constant G at the origin = ?

Solution :

We know that the gravitational potential of two masses $m_1$ and $m_2$ at a distance r is given as :

$= \frac{Gm_1 m_2}{r}$

Here , G is gravitational constant

So, according to this formula the gravitational potential for the given masses at origin will be given as :

= $2\times (\frac{G\times 1 \times 1}{1} + \frac{G\times 1 \times 1}{2}+\frac{G\times 1 \times 1}{4} +......+ \frac{G\times 1 \times 1}{\infty})$

$= 2 \times (\frac{G}{1}+\frac{G}{2}+ \frac{G}{4}+........)$

Here it is forming a series of infinite GP, Since the formula for sum of infinite GP is given as = $\frac {a}{1-r}$

where a is 1st term and r is the common ratio .

So, here sum of the GP is :

$=\frac{(\frac{G}{1})}{(\frac{1}{2}) }$

= 2G

So , total gravitational potential at origin is $2\times 2G$ = 4G

A hair dryer with a resistance of 9.6 ohms operates at 120 volts for 2.5 minutes. the total electrical energy used by the dryer during this time interval is

Asked by maham237 @ 13/01/2021 in Physics viewed by 1206 persons

Mind map for light reflection and refraction class 10

Asked by admin @ 23/08/2021 in Physics viewed by 1148 persons

The african cicada is the world's loudest insect, producing a sound intensity level of 107 db at a distance of 0.50 m. what is the intensity of its sound (in w/m2) as heard by someone standing 3.1 m away? express your answer in watts per meter squared.

Asked by maham237 @ 10/01/2021 in Physics viewed by 1101 persons

A thief runs at a speed of 10m s

Asked by admin @ 23/08/2021 in Physics viewed by 1097 persons

A 5.8 x 10 4 watt elevator motor can lift

Asked by maham237 @ 20/06/2021 in Physics viewed by 1082 persons

An infinite number of masses each of one kg

Similar Questions

Infinite number of bodies each of mass 2kg

How did the one-child policy result in large numbers of undocumented chinese?

Isotopes of the same element have the same mass number

What is the mass number of an element equal to

The mass number of an atom can be calculated from

The mass number of an atom is the number of

1 what is the number one selling cd this week

Calculate the mass of one atom of oxygen

A particle of unit mass undergoes one dimensional

Every counting number has an infinite number of

Move one matchstick to make a biggest number

A solid sphere of mass 2 kg is resting

First 30 elements with atomic number and mass number

A block of mass 10 kg moving with acceleration

A block of mass root 2 kg is released

Most viewed questions in Physics

Jeevandeep health and physical education std 10 answers pdf

Hc verma physics class 9 solutions of describing motion

How to leave nightmare land answer key

Base area and stability of some objects with different shapes

Which of the following statements about safe lifting are correct

Porous water-absorbing mass of fibers

Absorption of water by filter paper is due to

A composite wire of uniform diameter 3mm

At a distance l 400m from the traffic light

A rocket of mass m is launched straight up with thrust f⃗ thrust.

A hair dryer with a resistance of 9.6 ohms operates at 120 volts for 2.5 minutes. the total electrical energy used by the dryer during this time interval is

Mind map for light reflection and refraction class 10

The african cicada is the world's loudest insect, producing a sound intensity level of 107 db at a distance of 0.50 m. what is the intensity of its sound (in w/m2) as heard by someone standing 3.1 m away? express your answer in watts per meter squared.

A thief runs at a speed of 10m s

A 5.8 x 10 4 watt elevator motor can lift