Mohit has a mass of 50.0 kg and weighs 554 N on Saturn. Calculate Saturn’s radius.
To calculate Saturn's radius, we can use the formula for gravitational force:
F = (G * m1 * m2) / r^2
Where:
F = gravitational force
G = gravitational constant (6.67430 × 10^-11 N(m/kg)^2)
m1 = mass of object 1 (Mohit's mass, 50.0 kg)
m2 = mass of object 2 (Saturn's mass)
r = distance between the center of the two objects (Saturn's radius, what we're trying to find)
From the problem, we are given that Mohit weighs 554 N on Saturn. Weight is the gravitational force acting on an object, so we can replace F with 554 N.
Let's rearrange the formula to solve for r:
r^2 = (G * m1 * m2) / F
Plugging in the known values:
r^2 = (6.67430 × 10^-11 N(m/kg)^2 * 50.0 kg * m2) / 554 N
To solve for r, we need to know Saturn's mass, m2. However, this information is not given in the problem. Without Saturn's mass, we cannot calculate its radius.
To calculate Saturn's radius, we need to use the equation for gravitational force:
F = (G * m1 * m2) / r^2
Where:
F = gravitational force
G = gravitational constant (6.67 x 10^-11 Nm^2/kg^2)
m1 = mass of one object (in this case, Mohit's mass)
m2 = mass of the other object (in this case, Saturn's mass)
r = distance between the centers of the two objects (in this case, Saturn's radius)
We can rearrange the equation to solve for r:
r = sqrt((G * m1 * m2) / F)
Substituting the given values into the equation:
r = sqrt((6.67 x 10^-11 Nm^2/kg^2 * 50.0 kg * m2) / 554 N)
As we don't know Saturn's mass (m2), we cannot find the exact radius. The mass of Saturn is approximately 5.68 x 10^26 kg, so we could approximate the radius using this value. However, in this step-by-step response, we'll leave it as an unknown variable.