Question

If radius of earth is increased or decreased by n%, mass remaining constant, then find
the percentage increase or decrease in value of acceleration due to gravity.​

Answer 1

Answer:

2n%

Explanation:

⇒Acceleration due to gravity is given by,

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

⇒where,

• g=acceleration due to gravity
• G=gravitational constant
• m=mass of earth
• r=radius of earth.

⇒'G' is constant and given that 'm' is also a constant. then variation in g only depends on 'r'

⇒So, we can write,

$g \: \alpha \: {r}^{2}$

⇒Let's take

• %g/g= percentage error in acceleration due to gravity
• %r/r= percentage error in radius=n (given)

⇒then,

$\frac{\%g}{g} = 2 \times \frac{\%r}{r?} \\ = 2 \times n \\ = 2n\%$

hope it helps...!!