an object weighs 10N on earth .what is the objects weight on a planet one tenth the earths mass and one half its radius?

Weight is mass m times acceleration due to gravity g, which is given by g=GMm/R^2 where M and R are mass & radius of Earth and G is Universal Gravitational Constant.

For new planet, g`=G(0.1Mm/(R/2)^2
=0.1GMm/R^2/4
=GMm(0.1x4)/R^2=0.4GMm/R^2
Hence g/g`=0.4, which means the weight on the new planet will be 10X0.4=4N.

Well, on a serious note, the weight of an object depends on the planet's gravitational pull. So, if we're talking about a planet one-tenth the Earth's mass and one-half its radius, we can assume its gravity is also one-tenth of Earth's.

Therefore, if the object weighs 10N on Earth, on this planet its weight would be 10N multiplied by one-tenth, which is... 1N! That's like a feather on steroids!

To determine the object's weight on a planet with one-tenth the earth's mass and one-half its radius, we need to apply the formula for gravitational force:

F = (G * m1 * m2) / r^2

Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2)
m1 is the mass of the first object (the planet)
m2 is the mass of the second object (the object)
r is the distance between the centers of the two objects

Let's proceed step-by-step:

Step 1: Determine the mass of the planet.
Given that the mass of the planet is one-tenth the mass of the earth, we can write:
m1 = (1/10) * mEarth

Step 2: Determine the distance between the center of the planet and the center of the object.
Given that the radius of the planet is half the radius of the earth, we can write:
r = (1/2) * rEarth

Step 3: Calculate the gravitational force on the object.
Plugging in the values into the formula, we have:
F = (G * m1 * m2) / r^2

Substituting the values:
F = (G * (1/10) * mEarth * m2) / ((1/2) * rEarth)^2

Step 4: Simplify and convert.
By simplifying the equation, we get:
F = (1/40) * (G * (2 * mEarth) * m2) / (rEarth)^2

Since the weight of the object on Earth is given as 10N:
10N = (1/40) * (G * (2 * mEarth) * m2) / (rEarth)^2

Therefore, the weight of the object on a planet with one-tenth the earth's mass and one-half its radius would be 10N.

To find the object's weight on a planet one-tenth the mass and one-half the radius of Earth, we need to understand the relationship between weight, mass, and gravitational force.

The weight of an object is given by the formula:

Weight = Mass x Gravitational Acceleration

On Earth, the gravitational acceleration is approximately 9.8 m/s^2. Therefore, if an object weighs 10N, we can calculate its mass using the formula:

Weight = Mass x Gravitational Acceleration

10N = Mass x 9.8 m/s^2

Solving for mass:

Mass = 10N / 9.8 m/s^2

Mass ≈ 1.02 kg

Now, let's consider the planet with one-tenth the mass and one-half the radius of Earth.

The mass of this planet would be one-tenth of Earth's mass, which is:

Planet's Mass = (1/10) x Earth's Mass ≈ (1/10) x 5.972 × 10^24 kg

Planet's Mass ≈ 5.972 × 10^23 kg

The radius of this planet would be one-half of Earth's radius, which is:

Planet's Radius = (1/2) x Earth's Radius ≈ (1/2) x 6,371 km

Planet's Radius ≈ 3,185.5 km

Now, we can determine the gravitational acceleration on the planet using the formula:

Gravitational Acceleration = (Gravitational Constant x Planet's Mass) / (Planet's Radius)^2

The Gravitational Constant is approximately 6.674 × 10^-11 N(m^2/kg^2).

Gravitational Acceleration = (6.674 × 10^-11 N(m^2/kg^2) x 5.972 × 10^23 kg) / (3,185.5 km)^2

Gravitational Acceleration = 0.06674 m/s^2

Finally, we can calculate the object's weight on this planet using the same formula as before:

Weight = Mass x Gravitational Acceleration

Weight = 1.02 kg x 0.06674 m/s^2

Weight ≈ 0.068 N

Therefore, the object would weigh approximately 0.068N on a planet one-tenth the mass and one-half the radius of Earth.