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Physics Part-I

Gravitation

Two stars each of one solar mass (=2 10^{30} kg) are approach

Physics Part-I

Class 11

NCERT

Chapter 1: Physical World

16 questions

Chapter 2: Units and Measurements

51 questions

Chapter 3: Motion in Straight Line

50 questions

Chapter 4: Motion in a Plane

43 questions

Chapter 5: Laws of motion

52 questions

Chapter 6: Work, Energy and Power

41 questions

Chapter 7: System of Particles and Rotational Motion

45 questions

Chapter 8: Gravitation

33 questions

A satellite orbits the earth at a height of 400 km above the surface. How much energy must be expended to rocket the satellite out of the earth's gravitational influence? Mass of the satellite

= 200 k g

; mass of the earth

= 6.0 \times 1 0^{24} k g

; radius of the earth

= 6.4 \times 1 0^{6} m

; G =

6.67 \times 1 0^{- 11} N m^{2} k g^{- 2}

Two stars each of one solar mass

(= 2 \times 1 0^{30} k g)

are approaching each other for a head on collision. When they are a distance

1 0^{9} km

, their speeds are negligible. What is the speed with which they collide ? The radius of each star is

1 0^{4} km

. Assume the stars to remain undistorted until they collide. (Use the known value of G).

Two heavy spheres each of mass 100 kg and radius 0.10 m are placed 1.0 m apart on a horizontal table. What is the gravitational force and potential at the mid point of the line joining the centres of the spheres ? Is an object placed at that point in equilibrium? If so, is the equilibrium stable or unstable ?

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Two stars each of one solar mass $(= 2 \times 1 0^{30} k g)$ are approaching each other for a head on collision. When they are a distance $1 0^{9} km$ , their speeds are negligible. What is the speed with which they collide ? The radius of each star is $1 0^{4} km$ . Assume the stars to remain undistorted until they collide. (Use the known value of G).

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Physics Part-I (NCERT)

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Two stars each of one solar mass

(= 2 \times 1 0^{30} k g)

are approaching each other for a head on collision. When they are a distance

1 0^{9} km

, their speeds are negligible. What is the speed with which they collide ? The radius of each star is

1 0^{4} km

. Assume the stars to remain undistorted until they collide. (Use the known value of G).

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Discuss this question LIVE

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Text solutionVerified

Given:

The mass of a star is,

M = 2 \times 1 0^{30} k g

The radius of each star is,

R = 1 0^{4} km = 1 0^{7} m

Distance between two stars is,

r = 1 0^{9} km = 1 0^{12} m

As the stars are separated by a distance, initially the stars will have gravitational potential energy.

Total energy of the system of two stars is given by:

E = - \frac{GMM}{r}

......(1)

Now as the stars move towards each other they gain the kinetic energy.

Let velocity of the stars when they are about to collide be

v

and at collision the distance between the centers of the stars

= 2 R

The total kinetic energy of the stars system

E_{k} = \frac{1}{2} M v^{2} + \frac{1}{2} M v^{2} = M v^{2}

and the total potential energy of the two stars system close to each other is:

E_{p} = - \frac{GMM}{2 R}

Thus, the total energy of the two stars just before collision

E_{t} = M v^{2} - \frac{GMM}{2 R}

........(2)

Since the energy remains conserved, the initial and final energy will be same.

M v^{2} - \frac{GMM}{2 R} = - \frac{GMM}{r}

v^{2} = \frac{GM}{2 R} - \frac{GM}{r}

= 6.67 \times 1 0^{- 11} \times 2 \times 1 0^{30} (\frac{1}{2 \times 1 0 ^{7}} - \frac{1}{1 0 ^{12}})

\approx 6.67 \times 1 0^{12}

∴ v = 2.58 \times 1 0^{6} m / s

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Practice more questions from Physics Part-I (NCERT)

A satellite orbits the earth at a height of 400 km above the surface. How much energy must be expended to rocket the satellite out of the earth's gravitational influence? Mass of the satellite

= 200 k g

; mass of the earth

= 6.0 \times 1 0^{24} k g

; radius of the earth

= 6.4 \times 1 0^{6} m

; G =

6.67 \times 1 0^{- 11} N m^{2} k g^{- 2}

Two stars each of one solar mass

(= 2 \times 1 0^{30} k g)

are approaching each other for a head on collision. When they are a distance

1 0^{9} km

, their speeds are negligible. What is the speed with which they collide ? The radius of each star is

1 0^{4} km

. Assume the stars to remain undistorted until they collide. (Use the known value of G).

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Question Text	Two stars each of one solar mass $(= 2 \times 1 0^{30} k g)$ are approaching each other for a head on collision. When they are a distance $1 0^{9} km$ , their speeds are negligible. What is the speed with which they collide ? The radius of each star is $1 0^{4} km$ . Assume the stars to remain undistorted until they collide. (Use the known value of G).
Topic	Gravitation
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	67

Text solutionVerified

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