Question

A sphere of radius R and mass M has density ρ. The magnitude of gravitational field at r= R/2 is pGM/qR², where p and q are integers In their lowest forms. The value of (p+q) is​

Answer 1

The value of p + q is 5

Explanation:

Given:

For a sphere of mass M and radius R

Magnitude of gravitational field at r = R/2 is

pGM/qR²

To find out:

The value of p + q

Solution:

We know that gravitational field at a distance r from centre is given by

$g=\frac{GM}{r^2}$

Now if r = R/2

Then

$g=\frac{GM}{(R/2)^2}$

$\implies g=\frac{3GM}{R^2}$

Comparing the above with $\frac{pGM}{R^2}$

We get

p = 4, q = 1

Therefore,

p + q = 4 + 1 = 5

Hope this answer is helpful.

Know More:

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Answer 2

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