Question

Two objects having mass in the ratio 1 : 4 are dropped from the same height above the ground. The relation between their velocity when they strike the ground is​

Answer 1

Answer:

If two objects with different masses are dropped from same height then they have same velocities or not?

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We can determine the velocity in this situation by using the well known equations of motion. In the equation v²=u²+2as , u=0 since the object is dropped from a particular height, a=-g the acceleration due to gravity downwards towards the Earth with vertically up direction taken as positive, s=h the height from which the objects are dropped. The equation after substitution gives the final velocity (or downward velocity at any point above which the point of release is at a particular height ‘h') as v=-(2gh)½ (since the height or distance travelled by the object is negative as it is in the vertically downward direction and the velocity attained is also vertically downwards). This shows that if there are no external forces acting such as the resistance provided by the atmosphere, the velocity attained is independent of mass of the object.

Explanation:

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Answer 2

Same velocity (option !)

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]