(a)
The mass of a hypothetical spherical asteroid.

Answer to Problem 11Q
The mass of the hypothetical spherical asteroid is
Explanation of Solution
Given:
The diameter of the asteroid is
The average density of the asteroid is
Concept used:
The density of a body is defined as the total mass of it present in the total volume of the substance in the region of space.
Write the expression for the density of the body.
Rearrange the above expression for
Here,
Write the expression for the volume of the spherical asteroid.
Here,
Substitute
Calculation:
Substitute
Conclusion:
Thus, the mass of the hypothetical spherical asteroid is
(b)
The speed required to escape from the surface of the asteroid.

Answer to Problem 11Q
The escape velocity of the asteroid is
Explanation of Solution
Given:
The mass of the hypothetical spherical asteroid is
The diameter of the asteroid is
Concept used:
According to the law of conservation of mechanical energy, the total mechanical energy of the system is always a constant and therefore, the sum of the kinetic and the potential energy is also a constant, provided only conserved forces are applied.
Write the expression for conservation of mechanical energy as the sum of the kinetic and the potential energy.
Here,
Write the expression for kinetic energy.
Here,
Write the expression for the gravitational potential energy.
Here,
Substitute
Simplify the above expression.
Here,
As a body escapes with velocity, the only force on it is the gravitational force of the massive body and when it goes out of the gravitational pull, the force on it is nearly zero. Therefore, it is considered to be at infinity and final velocity
Substitute
Simplify and rearrange the above expression for
Here,
Substitute
Calculation:
Substitute
Conclusion:
Thus, the escape velocity of the asteroid is
(c)
The condition if an astronaut starts to jog on the surface of the asteroid with a velocity of

Answer to Problem 11Q
The astronaut will escape out from the gravitational field of the asteroid.
Explanation of Solution
Concept used:
The escape velocity of the asteroid is
Conclusion:
Thus, the astronaut will escape out from the gravitational field of the asteroid.
Want to see more full solutions like this?
Chapter 7 Solutions
UNIVERSE (LOOSELEAF):STARS+GALAXIES
- Before attempting this problem, review Conceptual Example 7. The intensity of the light that reaches the photocell in the drawing is 160 W/m², when 0 = 18°. What would be the intensity reaching the photocell if the analyzer were removed from the setup, everything else remaining the same? Light Photocell Polarizer Insert Analyzerarrow_forwardThe lifetime of a muon in its rest frame is 2.2 microseconds. What is the lifetime of the muon measured in the laboratory frame, where the muon's kinetic energy is 53 MeV? It is known that the rest energy of the muon is 106 MeV. Select one: O 4.4 microseconds O 6.6 microseconds O 3.3 microseconds O 1.1 microsecondsarrow_forwardThe Lagrangian of a particle performing harmonic oscil- lations is written in the form L = ax² - Bx² - yx, where a, and are constants. What is the angular frequency of oscillations? A) √2/a B) √(+2a)/B C) √√Ba D) B/αarrow_forward
- The mean temperature of the Earth is T=287 K. What would the new mean temperature T' be if the mean distance between the Earth and the Sun was increased by 2%? Select one: ○ 293 K O 281 K ○ 273 K 284 Karrow_forwardTwo concentric current-carrying wire loops of radius 3 cm and 9 cm lie in the same plane. The currents in the loops flow in the same direction and are equal in magnitude. The magnetic field at the common center of the loops is 50 mT. What would be the value of magnetic field at the center if the direction of the two currents was opposite to each other (but their value is kept constant)? Select one: ○ 20 mT ○ 10 mT O 15 mT ○ 25 mTarrow_forwardAn ideal coil of inductivity 50 mH is connected in series with a resistor of 50 ohm. This system is connected to a 4.5 V battery for a long time. What is the current in the circuit? Select one: O 45 mA ○ 90 mA 00 mA O 150 mAarrow_forward
- There are two thin-walled spherical shells made from the same material, the radius of the smaller shell is half of the radius of the larger one. The thickness of the walls is the same. Denote the moment of inertia (with respect to the center) of the larger shell by I₁, and that of the smaller one by 12. What is the ratio I₁/12? Select one: ○ 8 O 16 O 4 ○ 32arrow_forwardA swimming pool has dimensions 20.0 m X 20.0 m and a flat bottom. The pool is filled to a depth of 3.00 m with fresh water. By what force does the water push each of the sidewalls? Density of water is 1000 kg/m³. Select one: ○ ~ 900 KN о ~ 2 ~ 1800 kN 600 kN 1500 kNarrow_forwardFrom one corner of a thin homogeneous square metal sheet with sides of L = 20 cm is cut an L/2 square sheet as shown in the figure. Approximately how far away is the centre of mass of the resulting shape from the centre P of the original square? P ○ 24 mm ○ 42 mm ○ 32 mm ○ 16 mmarrow_forward
- 20:19 Vol 69% + WiFi2 nothing happens to the nqara lever more the container (d) none of these 33. Statement I: The internal energy of a solid substance increases during melting.4_03-04-2025_QP.pdf Statement II: The molecules have greater kinetic energy in a liquid. Statement I and Statement II are true and the (a) Statement II is the correct explanation of Statement I. Statement I and Statement II are true but the (b) Statement II is not the correct explanation of Statement I. (c) Statement I is true but Statement II is false. (d) Statement I and Statement II are false. 34. Select correct statement related to heat 35. (a) Heat is possessed by a body (b) (c) Hot water contains more heat as compared to cold water Heat is the energy which flows due to temperature difference (d) All of these Two liquids A and B are at 32°C and 24°C. When mixed in equal masses the temperature of the mixture is found to be 28°C. Their specific heats are in the ratio of: (a) 3:2 (c) 1:1 (b) 2:3 (d) 4:3 36.…arrow_forwardThe skid loader shown has a mass of 1.28 Mg and in the position shown the center of mass is at G. There is a 255 kg barrel in the bucket with its center of mass at GB. The horizontal distance between the barrel's center of mass and the front wheels is d = 1.33 m. The horizontal distance between the front wheels and rear wheels is w = 0.55 m. The bucket arm is held horizontal between D and E and the pair of hydraulic cylinders creates angle /EDC of 0 = 32 degrees. 1.25 m GB D 60000 A G B E C 0.15 m 0.5 m d W i. Determine the reaction force on the pair of wheels at the front of the skid loader at A. ii. Determine the reaction force on the pair of wheels at the rear of the skid loader at B. iii. Determine the magnitude of the compressive force in a single hydraulic cylinder CD. Note that there are two hydraulic cylinders, one on each side of the skid loader. iv. Determine the magnitude of the reaction force on a single pin that attaches the bucket assembly to the skid loader chassis at E.…arrow_forwardThe truss structure below is subjected to three forces as shown. P₁ = 7.5 kN P2 = 10.5 kN P3 = 6.5 kN h = 3.5 m w= 2.7 m A W B F E P3 P1 W C P2 W Ꭰ h i. Identify any Zero Force Members. ii. Calculate the support reaction forces at A and D. iii. Calculate the magnitude of the force in members EF, CF, BC, DE, and CD and state if these members are in tension or compression.arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityGlencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-Hill
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningClassical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningFoundations of Astronomy (MindTap Course List)PhysicsISBN:9781337399920Author:Michael A. Seeds, Dana BackmanPublisher:Cengage Learning





