Question

A ball of mass m = 20 kg released from height h = 10m falls on the Earth's surface. The speed of the Earth when the ball reaches the Earth's surface is ______ × 10^-23 m/s.

Options

• 4.88

• 3.56

• 4.66

• 4.11

Answer 1

A ball of mass m = 20 kg released from height h = 10m falls on the Earth's surface. The speed of the Earth when the ball reaches the Earth's surface is 4.66 × 10^-23 m/s.

Explanation:

m₂ = 6 × 10²⁴ kg mass of earth

v₁ when the ball reaches earth surface = `sqrt(2gh)`

= `sqrt(2 xx 9.8 xx 10)`

`v_1 = sqrt(196) = 14` m/s.

Because no external force exists, the velocity of the centre of mass must remain zero.

`(m_1vecv_1 + m_2vecv_2)/(m_1 + m_2) = 0`

`m_2vecv_2 = -m_1vecv_1`

`v_2 = (20 xx 14)/(6 xx 10^24)`

= `4.66 xx 10^-23` m/s