Question

wo masses of bodies in the ratio 1 : 4 are dropped from a tower. find the ratio og velocities when these bodies strike the ground and also find the ratio of the forces on these bodies​

Answer 1

Two masses of bodies in the ratio 1 : 4 are dropped from tower.

we have to find the ratio of velocities when bodies strike the ground and also find the ratio of the forced on these bodies.

if a body is dropped from the top of tower of height h, velocity of body , v = √2gh [ i.e., velocity doesn't depend on mass ]

so, ratio of velocities of bodies is 1 : 1 because they are dropped from same height.

now force = mass × acceleration.

as accelerations acting on both bodies are same.i.e., g [ acceleration due to gravity]

so, force ∝ mass

i.e., F₁/F₂ = m₁/m₂ = 1/4

so ratio of forces on these bodies is 1 : 4.

Answer 2

Velocity remains same

1 : 4

Explanation:  Using the equation of motion:  v = u + at

           For 1st body, a = g, u = 0

⇒ v₁ = 0 + gt₁    ⇒ v₁ = gt₁

           For 2nd body, a = g, u = 0

⇒ v₂ = 0 + gt₂    ⇒  v₂ = gt₂

Using, S = ut + 1/2 at²,

⇒ S₁ = 0(t) + g(t₁)²/2   ⇒ S₁ =  g(t₁)²/2

⇒ S₂ = 0(t) + g(t₂)²/2   ⇒ S₂ =  g(t₂)²/2

  But since they are dropped form same height, S₁ = S₂:

⇒ g(t₁)²/2 = g(t₂)²/2

⇒ t₁ = t₂    

Hence,  v₁ = gt₁  &  v₂ = gt₂

 v₁ = gt₁ = gt₂ = v₂       [t₁ = t₂]

(ii)   F = ma  , let masses be x and 4x

For 1st body, F₁ = 1xa = xa

For 2nd bod, F₂ = 4xa

Ratio of forces = (xa):(4xa) = 1 : 4