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The radius of earth is about 6400 km and that of mars is 3200 km. The mass of earth is about 10 times mass of mars. An object weighs 200 N on the surface of earth. Its weight on the surface of mars will be
The weight of an object is the force it experiences due to gravity, which depends on the gravitational field of the celestial body it is on. The weight of an object on a planet's surface is directly proportional to the mass of the planet and inversely proportional to the square of the planet's radiuRead more
The weight of an object is the force it experiences due to gravity, which depends on the gravitational field of the celestial body it is on. The weight of an object on a planet’s surface is directly proportional to the mass of the planet and inversely proportional to the square of the planet’s radius.
In this case, the object weighs 200 N on Earth. The Earth’s radius is approximately 6400 km, and its mass is about 10 times that of Mars. Mars has a smaller radius of approximately 3200 km. The gravitational pull experienced by the object on Mars depends on the ratio of Mars’ mass and radius compared to Earth’s. Since Mars is less massive and smaller in size, the gravitational force on its surface is weaker.
Taking into account the relative differences in mass and radius, the weight of the object on Mars is calculated to be 80 N. This is significantly less than its weight on Earth due to Mars’ smaller mass and lower surface gravity. This concept highlights how weight varies on different planets, even though the object’s mass remains the same, showcasing the influence of planetary characteristics on gravitational forces.
See lessA body of weight 72 N moves from the surface of earth at a height half of the radius of earth, then gravitational force exerted on it will be
The gravitational force on a body depends on its weight at the Earth's surface and its distance from the Earth's center. At the Earth's surface, the weight of the body is 72 N. If the body moves to a height equal to half the Earth's radius above the surface, the distance from the Earth's center incrRead more
The gravitational force on a body depends on its weight at the Earth’s surface and its distance from the Earth’s center. At the Earth’s surface, the weight of the body is 72 N. If the body moves to a height equal to half the Earth’s radius above the surface, the distance from the Earth’s center increases, and the gravitational force decreases.
Gravitational force is inversely proportional to the square of the distance from the center of the Earth. At the new height, the total distance from the Earth’s center becomes 1.5 times the Earth’s radius. Since the gravitational force weakens with the square of this distance, it decreases significantly compared to the force at the surface.
With this, after considering the relation of the gravitational force with distance, it can be deduced that at this height, the gravitational force acting on the body will be diminished to 32 N. This again illustrates that a body experiencing lesser gravitational force from an Earth as one increases distance from Earth’s core. Furthermore, the nature of forces with the inversely proportional law will govern how a gravitational force functions with changing distances; therefore, this rule is highly valued in both physics and astronomy.
See lessThe acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on planet B. A man jumps to a height of 2 m on the surface of A. What is the height of jump by the same person on the planet B?
The height a person can jump is inversely related to the acceleration due to gravity on the planet’s surface. This relationship means that if the gravitational pull is weaker, the person can jump to a greater height, as less force is pulling them back down. In this scenario, the acceleration due toRead more
The height a person can jump is inversely related to the acceleration due to gravity on the planet’s surface. This relationship means that if the gravitational pull is weaker, the person can jump to a greater height, as less force is pulling them back down.
In this scenario, the acceleration due to gravity on planet A is nine times greater than on planet B. On planet A, the person can jump to a height of 2 meters. When the same person jumps on planet B, where gravity is weaker, they can achieve a significantly higher jump because the reduced gravitational force allows their upward motion to last longer before being pulled back down.
Given the relationship between jump height and gravity, the height of the jump on planet B will be directly proportional to the reduction in gravity compared to planet A. Since planet A’s gravity is nine times stronger, the jump height on planet B will be nine times greater than on planet A. Therefore, the person will jump to a height of 18 meters on planet B. This demonstrates the impact of gravitational differences on physical activities, such as jumping, and highlights how gravity varies across celestial bodies.
See lessIf the gravitational force between two objects were proportional to 1/R (and not as 1/R²), where R is the distance between them, then a particle in a circular path (under such a force) would have its orbital speed v, proportional to
If the gravitational force between two objects were proportional to 1/R instead of 1/R², the dynamics of objects in circular orbits would be very different. In such a case, the force acting on a particle in a circular orbit would decrease less rapidly with increasing distance R. This would change thRead more
If the gravitational force between two objects were proportional to 1/R instead of 1/R², the dynamics of objects in circular orbits would be very different. In such a case, the force acting on a particle in a circular orbit would decrease less rapidly with increasing distance R. This would change the dependence of the orbital speed of the particle on its distance from the center of attraction.
For an object in stable circular orbit, the necessary centripetal force for maintaining its orbit has to be supplied by the gravitational force. Gravitational force that depends on 1/R, the usual dependency of necessary orbital speed on R is broken. For this case, orbital speed in terms of given condition leads to a value of v not depending on R. This means that the orbital speed is independent of the distance from the center of attraction.
This behavior is in contrast to the 1/R² dependence of the actual gravitational force, where the orbital speed decreases with an increase in distance. The hypothetical 1/R force would result in strange orbital dynamics, as particles would have the same speed at all distances, which would fundamentally change the structure and stability of orbits in such a system.
See lessTwo particles of equal mass go around a circle of radius R under the action of their mutual gravitational attraction. The speed v of each particle is
When two particles of equal mass revolve about a common centre of mass under their mutual gravitational attraction, the balance between the gravitational force and the centripetal force for circular motion dictates their motion. Since masses are equal, the centre of mass lies at the midpoint on theRead more
When two particles of equal mass revolve about a common centre of mass under their mutual gravitational attraction, the balance between the gravitational force and the centripetal force for circular motion dictates their motion. Since masses are equal, the centre of mass lies at the midpoint on the line joining the two particles. Each particle revolves about the centre of mass in a circular path of radius R/2.
The gravitational force between the particles is what furnishes them with the required centripetal force. The gravitational force depends upon the masses of the particles and the distance separating them, which is given by R. On the other hand, centripetal force depends upon the mass of each particle, the orbital speed v, and the radius of their circular path.
From the equality of gravitational and centripetal forces, it follows that the orbital velocity of each particle is as follows: v = 1/2 √(Gm/R) It follows that speed of each particle is proportional to the square root of the constant of gravitation G and mass of the particle m and inversely proportional to the square root of R. The final expression for the speed is given by v = 1/2 √(Gm/R), which shows the relationship between mass, radius, and speed in this two-body system.
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