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xz_007 [3.2K]
3 years ago
14

The gravitational force exerted by the planet Earth on a unit mass at a distance r from the center of the planet is:

Mathematics
1 answer:
jolli1 [7]3 years ago
8 0

Answer:

Yes, F is a continuous function of r

Step-by-step explanation:

We are given that

When r<R

F(r)=\frac{GMr}{R^3}

r\geq R

F(r)=\frac{GM}{r^2}

Where M=Mass of the earth

R=Radius of earth

G=Gravitational constant

We have to find the function is continuous of r or not.

LHL

\lim_{r\rightarrow R-}\frac{GMr}{R^3}=\frac{GMR}{R^3}=\frac{GM}{R^2}

RHL

\lim_{r\rightarrow R+}\frac{GM}{R^2}=\frac{GM}{R^2}

F(R)=\frac{GM}{R^2}

When a function is continuous at x=a

Then, LHL=RHL=f(a)

RHL==LHL=F(R)

Hence, the function is continuous of r.

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