Question

find the velocity of escape at the earth given that its radius is 6.4×10^6(6 is power) metre and the value of g at the surface is 9.8ms-2​

Answer 1

Answer:

• Velocity of escape at earth = 11200 m/s

Explanation:

Given:-

• The Radius of earth, r = 6.4 × 10^6 m
• value of acceleration due to gravity, g = 9.8 m/s^2

To find:-

• The Velocity of escape at Earth, v =?

Formula required:-

• Formula for escape velocity

        v = √( 2 Gm/r )

• Formula for acceleration due to gravity

        g = G m / r^2

[ Where v is the escape velocity, m is the mass of the body to be escaped, G is universal gravitational constant, r is the distance from the centre of mass/radius of the planet, g is the acceleration due to gravity ]

Solution:-

By the formula of acceleration due to gravity, We know

→ g = G m / r^2

→ G m = g r^2  .......equation (1)

Now,

substituting equation (1) in the formula of escape velocity

→ v = √( 2 Gm/r )

→ v = √( 2 gr^2/r )

→ v = √( 2 gr )

[ Putting values of g and r ]

→ v = √( 2 × 9.8 × 6.4 × 10^6 )

→ v = 11200 m/s

Therefore,

• The velocity of escape at the earth would be 11200 m/s.

Answer 2

Answer:

Refer to the given attachment -