Question

two partical held at the different hights a and b above the ground and allow to fall from rest the ratio of there velocity on reaching the ground is​

Answer 1

Given :-

▪ Two particles are held at different heights a and b respectively. They are allowed to fall from reat means initial velocity of both the particles = 0 m/s.

To Find :-

▪ Ratio of final velocities of the particles.

Solution :-

Since the particles are at a height of a and be respectively, so Displacement made by the particles are actually the heights they are held at.

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For Particle held at 'a' ,

Here, we have

• Displacement, s = a
• Acceleration = g
• Initial velocity = 0 m/s

Using 3rd equation of motion, we have

⇒ 2gs = v² - u²

⇒ 2ag = v² [ ∵ u = 0 ]

⇒ v = √2ag ...(1)

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For Particle held at 'b' ,

Similarly, we have

• Displacement, s = b
• Initial velocity, u = 0 m/s
• Acceleration = g

Using 3rd equation of motion, final velocity can be calculated as,

⇒ 2gs = v² - u²

⇒ 2gb = v² [ ∵ u = 0 ]

⇒ v₀ = √2gb ...(2)

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Now that we have found the final velocities of both the particles, Let us find the ratio now,

⇒ v / v₀ = √2ag / √2gb

⇒ v / v₀ = √( 2ag / 2gb)

⇒ v / v₀ = √(a / b)

⇒ v : v₀ = √a : √b

Hence, Ratio of the final velocities of the particles is √a : √b which are held at heights a and b respectively.