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Physics Part-I

Gravitation

A rocket is fired 'vertically' from the surface of mars with a

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 spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system ? Mass of the space ship = 1000 kg; mass of the sun =

2 \times 1 0^{30} k g

; mass of mars =

6.4 \times 1 0^{23} k g

; Radius of mars = 3395 km; Radius of the orbit of mars =

2.28 \times 1 0^{8} km

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

A rocket is fired 'vertically' from the surface of mars with a speed of

2 km s^{- 1}

. If 20% of its initial energy is lost due to martian atmospheric resistance, how far (in km) will the rocket go from the surface of mars before returning to it ? Mass of mars =

6.4 \times 1 0^{23} k g

; radius of mars = 3395 km;

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

Let the speed of the planet at the perihelion

P

in Figure and the Sun-planet distance SP be

r_{p}

. Relate

{r_{p}, v_{p}}

to the corresponding quantities at the aphelion

{r_{A}, v_{A}}

. Will the planet take equal times to traverse

B A C

and

CPB

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Question

Medium

Solving time: 4 mins

A rocket is fired 'vertically' from the surface of mars with a speed of $2 km s^{- 1}$ . If 20% of its initial energy is lost due to martian atmospheric resistance, how far (in km) will the rocket go from the surface of mars before returning to it ? Mass of mars = $6.4 \times 1 0^{23} k g$ ; radius of mars = 3395 km; $G = 6.67 \times 1 0^{- 11} N m^{2} k g^{- 2}$ .

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Updated on: Dec 30, 2022

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Physics Part-I (NCERT)

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A rocket is fired 'vertically' from the surface of mars with a speed of

2 km s^{- 1}

. If 20% of its initial energy is lost due to martian atmospheric resistance, how far (in km) will the rocket go from the surface of mars before returning to it ? Mass of mars =

6.4 \times 1 0^{23} k g

; radius of mars = 3395 km;

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

7 mins ago

Discuss this question LIVE

7 mins ago

Text solutionVerified

The total initial energy of the rocket and the planet system is the sum of the kinetic energy of the rocket and the gravitational energy of the system.

whereas the final energy will be the gravitational energy at a height H from the surface.

The total energy can be written as:

\frac{- GM m}{R} + (\frac{80}{100}) \frac{1}{2} m V^{2} = \frac{- GM m}{R + h} + 0

Simplify the above expression:

GM m (\frac{1}{R} - \frac{1}{R + h}) = 0.4 m (2 \times 1 0^{3})^{2}

\Rightarrow \frac{GM}{R} (1 - \frac{R}{R + h}) = 1.6 \times 1 0^{6}

= 1 - \frac{3.395 \times 1 0 ^{6} \times 1.6 \times 1 0 ^{6}}{6.67 \times 1 0 ^{- 11} \times 6.4 \times 1 0 ^{23}}

R + h = \frac{R}{0.873} = 3, \frac{395}{0.873} = 3, 888.9 km

So, the height attained by the rocket from the surface will be

H = 3, 888.9 - 3, 395 = 493.9 km

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Practice more questions from Physics Part-I (NCERT)

A spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system ? Mass of the space ship = 1000 kg; mass of the sun =

2 \times 1 0^{30} k g

; mass of mars =

6.4 \times 1 0^{23} k g

; Radius of mars = 3395 km; Radius of the orbit of mars =

2.28 \times 1 0^{8} km

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

A rocket is fired 'vertically' from the surface of mars with a speed of

2 km s^{- 1}

. If 20% of its initial energy is lost due to martian atmospheric resistance, how far (in km) will the rocket go from the surface of mars before returning to it ? Mass of mars =

6.4 \times 1 0^{23} k g

; radius of mars = 3395 km;

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

Let the speed of the planet at the perihelion

P

in Figure and the Sun-planet distance SP be

r_{p}

. Relate

{r_{p}, v_{p}}

to the corresponding quantities at the aphelion

{r_{A}, v_{A}}

. Will the planet take equal times to traverse

B A C

and

CPB

View all

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Question Text	A rocket is fired 'vertically' from the surface of mars with a speed of $2 km s^{- 1}$ . If 20% of its initial energy is lost due to martian atmospheric resistance, how far (in km) will the rocket go from the surface of mars before returning to it ? Mass of mars = $6.4 \times 1 0^{23} k g$ ; radius of mars = 3395 km; $G = 6.67 \times 1 0^{- 11} N m^{2} k g^{- 2}$ .
Updated On	Dec 30, 2022
Topic	Gravitation
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 5
Upvotes	485
Avg. Video Duration	14 min

Text solutionVerified

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