Question

At a place where value of g is less by 1% than its value on the surface of the earth. Radius of earth is 6400 km. The place is:
a) 64km below the surface of earth
b) 64km above the surface of earth
c) 30km above the surface of the earth
d) 32km below the surface of the earth.

Answer 1

Hello

We have to take out the at which place the value of g will be less than it’s value on surface of earth by 1% .  Now as the change is so less , i.e 1% we will use a special formula for finding out the height .

Formula :

⇒ $\boxed{\bold{g’=g(1 - \frac{2h}{R})}}$

This formula is used for small values , That is we use this formula when  h << R .  Here , R = radius earth ( 6400 km ) .

Now , according to the question, value of g is less by 1% than that of surface of earth So the  our new g that is ( g’ ) will be  = 0.99g

Putting the values in the formula , we get  :

⇒  $\boxed{\bold{0.99g=g(1 - \frac{2h}{6400})}}$

By solving above equation, ( g ) will be canceled out then only , h will be left so it will be linear equation in 1 variable and After solving it , the value of ( h ) → 32 Km

Hope It Helps You.     ^_^

Answer 2

Answer:

d) 32km below the surface of the earth.

Explanation:

At a place where value of g is less by 1% than its value on the surface of the earth. Radius of earth is 6400 km. The place is:

a) 64km below the surface of earth

b) 64km above the surface of earth

c) 30km above the surface of the earth

d) 32km below the surface of the earth ✓