# a satellite is orbiting around the earth with a period t. if the earth suddenly shrinks to half its radius without change in mass, the period of revolution of the satellite will be

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## A satellite is revolving around earth in its equatorial plane with a period T. If the radius of earth suddenly shrinks to half without change in the mass. Then, the new period of revolution will be

T = sqrt((GM)/(r)) T is independent of R, the radius of earth.

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A satellite is revolving aroun...

## A satellite is revolving around earth in its equatorial plane with a period `T`. If the radius of earth suddenly shrinks to half without change in the mass. Then, the new period of revolution will be

Updated On: 17-04-2022

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Text Solution

`8 T``2sqrt(2) T``2T``T`

`T = sqrt((GM)/(r))`Answer : D Solution :

`T` is independent of `R`, the radius of earth.Answer

Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

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## Very Important Questions

निम्नलिखित संख्याओ का वर्गमूल , भाग विधि से ज्ञात कीजिए : `{:((i)2304,(ii)4489,(iii)3481,(iv)529),((v)3249,(vi)1369,(vii)5776,(viii)7921),((ix)576,(x)1024,(x i)3136,(x ii)900):}`निम्नलिखित संख्याओं में से प्रत्येक में कम से कम कितना जोड़ा जाए कि एक पूर्ण वर्ग संख्या प्राप्त हों जाए । इस प्रकार प्राप्त वर्ग संख्याओ का वर्गमूल भी ज्ञात कीजिए : `{:((i)525,(ii)1750,(iii)252,(iv)1825),((v)6412,,,):}`एक विधालय में 500 विद्यार्थी हैं । पी. टी. के अभ्यास के लिए इन्हें इस तरह से खड़ा किया गया की पंक्तियों की संख्या कॉलम की संख्या के समान रहे । इस व्यवस्था को बनाने में कितने विद्यार्थियों को बाहर जाना होगा ?

अभाज्य गुणनखंड विधि द्वारा 13824 का घनमूल ज्ञात कीजिए ।

अभाज्य गुणनखंड विधि द्वारा निम्नलिखित में से प्रत्येक संख्या का घनमूल ज्ञात कीजिए : `{:((i),64,(ii),512,(iii),10648,(iv),27000),((v),15625,(vi),13824,(vii),110592,(viii),46656),((ix),175616,(x),91125,,,,):}`यदि किसी डिब्बे की मिठाई को 24 बच्चों में बांटा जाए, तो प्रत्येक बच्चे को 5 मिठाइयां मिलती हैं। यदि बच्चों की संख्या में 4 की कमी हो जाए, तो प्रत्येक बच्चे को कितनी मिठाइयां मिलेगीं?

## FAQs on Gravitation

**Introduction**

**KEPLER'S FIRST LAW**

**KEPLER'S SECOND LAW**

**KEPLER'S THIRD LAW**

**Defition Of G**

**DEDUCTION OF NEWTON'S LAW OF GRAVITATION FROM KEPLER'S LAWS**

**EVIDENCES IN SUPPORT OF NEWTON'S LAW OF GRAVITATION**

**Principle Of Superposition Of Gravitation**

**Inertial Mass**

**Gravitational Mass**

## A satellite is revolving around earth in its equatorial plane with a period T . lf the radius of earth suddenly shrinks to half its radius without change in the mass. Then, the new period of revolution will be

Click here👆to get an answer to your question ✍️ A satellite is revolving around earth in its equatorial plane with a period T . lf the radius of earth suddenly shrinks to half its radius without change in the mass. Then, the new period of revolution will be

Question

## A satellite is revolving around earth in its equatorial plane with a period T. lf the radius of earth suddenly shrinks to half its radius without change in the mass. Then, the new period of revolution will be

**A**

## 8T

**B**2

2 T

**C**

## 2T

**D**

## T

Medium Open in App Solution Verified by Toppr

Correct option is D)

Time period of revolution is dependent on:1. the mass of the planet around which the satellite is revolving M

2. the radius of the orbit of the satellite r

T=2π GM r 3 .

Since, mass of earth is not changed and radius of orbit is not changed, time period will remain the same. Time period does not depend on the radius of the planet around which the satellite is revolving.

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## A satellite is revolving around earth in its equatorial class 11 physics CBSE

A satellite is revolving around earth in its equatorial plane with a period T If the radius of earth suddenly shrinks to half its radius without change in the mass Then the new period of revolution will

A satellite is revolving around earth in its equatorial plane with a periodT T

. If the radius of earth suddenly shrinks to half its radius without change in the mass. Then, the new period of revolution will be

A. 8T 8T B. 2 2 – √ T 22T C. 2T 2T D. T T Answer Verified 163.5k+ views

**Hint:**The centrifugal force will be equal to the gravitational force between earth and satellite. Use this expression to understand the relation between the time period and the variables. Determine the change in time period if the radius of the planet changes.

**Formula used:**

mR ω 2 = GmM R 2 mRω2=GmMR2 ω= 2π T ω=2πT

**Complete step by step solution:**

Consider a satellite of mass

m m

revolving around earth of mass

M M

in a circular orbit. The gravitational force of attraction that exists between the two bodies will be equal to the centrifugal force that exists on the satellite due to its circular motion. It can be seen as,

mR ω 2 = GmM R 2 ω= GM R 3 − − − − √ mRω2=GmMR2ω=GMR3 Here, ω ω

is the angular velocity of the satellite and

R R

is the radius of orbit measured from the center of earth. The expression for time period of satellite is calculated as,

ω= 2π T T= 2π ω =2π R 3 GM − − − − √ ω=2πTT=2πω=2πR3GM

The above expression shows that the time period of the satellite is independent of the mass of the satellite and radius of the planet. The time period depends only on the mass of earth and the distance of satellite from the center of earth.

Now, the questions mention that the radius of earth is halved keeping the mass the same. We can see from the obtained expression for the time period that there will be no change on the time period of the satellite.

**Thus, the correct option is (D).**

**Note:**

Deduce the relation for the time period of the satellite correctly. Do not get confused between the mass of earth and mass of satellites. The radius of orbit is measured from the center of earth and should not be confused with the radius of earth.

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