The distance an object falls from rest through gravity is
D = (1/2) (g) (t²)
Distance = (1/2 acceleration of gravity) x (square of the falling time)
We want to see how the time will be affected if ' D ' doesn't change but ' g ' does. So I'm going to start by rearranging the equation to solve for ' t '.
D = (1/2) (g) (t²)
Multiply each side by 2 : 2 D = g t²
Divide each side by ' g ' : 2 D/g = t²
Square root each side: t = √ (2D/g)
Looking at the equation now, we can see what happens to ' t ' when only ' g ' changes:
-- ' g ' is in the denominator; so bigger 'g' ==> shorter 't' and smaller 'g' ==> longer 't' .
-- They don't change by the same factor, because 1/g is inside the square root. So 't' changes the same amount as √1/g does.
Gravity on the surface of the moon is roughly 1/6 the value of gravity on the surface of the Earth.
So we expect ' t ' to increase by √6 = 2.45 times.
It would take the same bottle (2.45 x 4.95) = 12.12 seconds to roll off the same window sill and fall 120 meters down to the surface of the Moon.
V o - initial velocity v = velocity at the maximum height, v² = v o² - 2 g h v = 0 0 = v o² - 2 g h v o² = 2 g h = 2 · 9.80 · 0.460 v o² = 9.052 v o = √9.052 = 3.004197 m/s ≈ 3 m/s
The relationship between the mass and the energy is given by Einstein formula as :
m is the mass of an atom
c is the speed of light
When an atom is formed, the energy gets absorbed. As a result mass will decrease as per Einstein's equation. So, the correct option is (c) "Energy is absorbed, so the mass is reduced".
