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The ratio of the heights from which two bodies are dropped is 3:5 respectively. The ratio of their final velocities is:
- a)9 : 25
- b)√ 3 : √ 5
- c)5 : 3
- d)√5 : √3
Correct answer is 'B'. Can you explain this answer?
Verified Answer
The ratio of the heights from which two bodies are dropped is 3:5 resp...
Velocity acquired by the two bodies falling from rest through a distance h is given as: v =
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The ratio of the heights from which two bodies are dropped is 3:5 resp...
Given:
Ratio of heights = 3:5
Let the heights be 3x and 5x respectively.
To find:
Ratio of final velocities
Solution:
The velocity with which a body falls from a height is given by the formula:
v² = u² + 2gh
Where,
v = final velocity
u = initial velocity (which is 0 in this case)
g = acceleration due to gravity
h = height
Since both the bodies are falling under the same acceleration due to gravity, we can write the above formula for both the bodies and compare the ratios:
For body 1:
v₁² = 2gh₁
v₁ = √(2gh₁)
For body 2:
v₂² = 2gh₂
v₂ = √(2gh₂)
We know that h₂/h₁ = 5/3 (given)
Therefore, h₂ = 5x and h₁ = 3x
Substituting the values of h₁ and h₂ in the above equations, we get:
v₁ = √(2g*3x) = √(6gx)
v₂ = √(2g*5x) = √(10gx)
Dividing v₂ by v₁, we get:
v₂/v₁ = √(10gx)/√(6gx) = √(10/6) = √(5/3)
Thus, the ratio of final velocities is 5:3, which is option B.
Ratio of heights = 3:5
Let the heights be 3x and 5x respectively.
To find:
Ratio of final velocities
Solution:
The velocity with which a body falls from a height is given by the formula:
v² = u² + 2gh
Where,
v = final velocity
u = initial velocity (which is 0 in this case)
g = acceleration due to gravity
h = height
Since both the bodies are falling under the same acceleration due to gravity, we can write the above formula for both the bodies and compare the ratios:
For body 1:
v₁² = 2gh₁
v₁ = √(2gh₁)
For body 2:
v₂² = 2gh₂
v₂ = √(2gh₂)
We know that h₂/h₁ = 5/3 (given)
Therefore, h₂ = 5x and h₁ = 3x
Substituting the values of h₁ and h₂ in the above equations, we get:
v₁ = √(2g*3x) = √(6gx)
v₂ = √(2g*5x) = √(10gx)
Dividing v₂ by v₁, we get:
v₂/v₁ = √(10gx)/√(6gx) = √(10/6) = √(5/3)
Thus, the ratio of final velocities is 5:3, which is option B.
Community Answer
The ratio of the heights from which two bodies are dropped is 3:5 resp...
For anything drop from certain height initial velocity (u)=0 so use equation v^2=u^2+2as here (a) is gravity that is (g)=10 now use this equation v^2=2gh because in above equation we take (u)=o
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The ratio of the heights from which two bodies are dropped is 3:5 respectively. The ratio of their final velocities is:a)9 : 25b)√ 3 : √ 5c)5 : 3d)√5 : √3Correct answer is 'B'. Can you explain this answer?
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