Question

A uniform solid sphere of radius R produces a gravitational acceleration ag on its surface. At what two distances from the centre of the sphere the acceleration due to gravity is a/4 ?

A. 4R, 0.50R
B. 2R, 0.25R
C. 3R, 0.33R
D. 2R, 0.50R

Answer 1

The two distances from the center of the uniform solid sphere where the gravitational acceleration is a/4 are 2R and 0.25R option B.

Step-by-step explanation:

To find the two distances from the center of the sphere where the acceleration due to gravity is a/4, we can use the formula for gravitational acceleration on the surface of a uniform solid sphere:

ag = (G × mass) / (radius^2)

where G is the gravitational constant, mass is the mass of the sphere, and radius is the radius of the sphere.

Setting the gravitational acceleration equal to a/4 and solving for the distances, we get:

r1 = (R √(4/π)) and r2 = (R √(16/π))

where R is the radius of the sphere given in the question.

Therefore, the answer is option B. 2R, 0.25R.