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Physics Part-I

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The planet Mars has two moons, phobos and delmos. (i) phobos h

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

Two uniform solid spheres of equal radii

R

, but mass

M

and

4 M

have a centre to centre separation

6 R

, as shown in Figure. The two spheres are held fixed. A projectile of mass

m

is projected from the surface of the sphere of mass

M

directly towards the centre of the second sphere. Obtain an expression for the minimum speed

v

of the projectile so that it reaches the surface of the second sphere.

The planet Mars has two moons, phobos and delmos. (i) phobos has a period 7 hours, 39 minutes and an orbital radius of

9.4 \times 1 0^{3} km

. Calculate the mass of mars. (ii) Assume that earth and mars move in circular orbits around the sun, with the martian orbit being

1.52

times the orbital radius of the earth. What is the length of the martian year in days?

Weighing the Earth : You are given the following data:

g = 9.81 ms^{- 2}

R_{E} = 6.37 \times 1 0^{6} m

, the distance to the moon

R = 3.84 \times 1 0^{8} m

and the time period of the moon's revolution is

27.3

days. Obtain the mass of the Earth

M_{E}

in two different ways.

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Question

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Solving time: 3 mins

The planet Mars has two moons, phobos and delmos. (i) phobos has a period 7 hours, 39 minutes and an orbital radius of $9.4 \times 1 0^{3} km$ . Calculate the mass of mars. (ii) Assume that earth and mars move in circular orbits around the sun, with the martian orbit being $1.52$ times the orbital radius of the earth. What is the length of the martian year in days?

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Updated on: Apr 20, 2023

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Physics Part-I (NCERT)

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The planet Mars has two moons, phobos and delmos. (i) phobos has a period 7 hours, 39 minutes and an orbital radius of

9.4 \times 1 0^{3} km

. Calculate the mass of mars. (ii) Assume that earth and mars move in circular orbits around the sun, with the martian orbit being

1.52

times the orbital radius of the earth. What is the length of the martian year in days?

7 mins ago

Discuss this question LIVE

7 mins ago

Text solutionVerified

(i)

T^{2} = k (R_{E} + h)^{3} (

where

k = 4 π^{2} / G M_{E})

with the sun's mass replaced by the martian mass

M_{m}

T^{2} = \frac{4 π ^{2}}{G M _{m}} R^{3}

M_{m} = \frac{4 π ^{2}}{G} \frac{R ^{3}}{T ^{2}}

= \frac{4 \times ( 3.14 ) ^{2} \times ( 9.4 ) ^{3} \times 1 0 ^{18}}{6.67 \times 1 0 ^{- 11} \times ( 459 \times 60 ) ^{2}}

M_{m} = \frac{4 \times ( 3.14 ) ^{2} \times ( 9.4 ) ^{3} \times 1 0 ^{18}}{6.67 \times ( 4.59 \times 6 ) ^{2} \times 1 0 ^{- 5}}

= 6.48 \times 1 0^{23} kg .

(ii) Once again Kepler's third law comes to our aid,

\frac{T _{M}^{2}}{T _{E}^{2}} = \frac{R _{MS}^{3}}{R _{ES}^{3}}

where

R_{MS}

is the mars -sun distance and

R_{ES}

is the earth-sun distance.

∴ T_{M} = (1.52)^{3/2} \times 365

= 684 days

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Practice more questions from Physics Part-I (NCERT)

Two uniform solid spheres of equal radii

R

, but mass

M

and

4 M

have a centre to centre separation

6 R

, as shown in Figure. The two spheres are held fixed. A projectile of mass

m

is projected from the surface of the sphere of mass

M

directly towards the centre of the second sphere. Obtain an expression for the minimum speed

v

of the projectile so that it reaches the surface of the second sphere.

The planet Mars has two moons, phobos and delmos. (i) phobos has a period 7 hours, 39 minutes and an orbital radius of

9.4 \times 1 0^{3} km

. Calculate the mass of mars. (ii) Assume that earth and mars move in circular orbits around the sun, with the martian orbit being

1.52

times the orbital radius of the earth. What is the length of the martian year in days?

Weighing the Earth : You are given the following data:

g = 9.81 ms^{- 2}

R_{E} = 6.37 \times 1 0^{6} m

, the distance to the moon

R = 3.84 \times 1 0^{8} m

and the time period of the moon's revolution is

27.3

days. Obtain the mass of the Earth

M_{E}

in two different ways.

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Question Text	The planet Mars has two moons, phobos and delmos. (i) phobos has a period 7 hours, 39 minutes and an orbital radius of $9.4 \times 1 0^{3} km$ . Calculate the mass of mars. (ii) Assume that earth and mars move in circular orbits around the sun, with the martian orbit being $1.52$ times the orbital radius of the earth. What is the length of the martian year in days?
Updated On	Apr 20, 2023
Topic	Gravitation
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 7
Upvotes	962
Avg. Video Duration	9 min

Text solutionVerified

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