Body 1 of mass 2 kg is dropped from a height h and body 2 of mass 6 kg is dropped from a height 4 h . Ratio of time taken by the bodies 1 and 2
Answers
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Question :-
Body 1 of mass 2 kg is dropped from a height h and body 2 of mass 6 kg is dropped from a height 4 h. Ratio of time taken by the bodies 1 and 2 is :
Answer :
Given
❥ Body 1 is of mass 2 kg and is dropped from a height h
❥ Body 2 is of mass 6 kg and is dropped from a height 4 h
Find :
Ratio of time taken by bodies 1 and 2
Here we go !
Solution :
Using Second equation of motion
s = u t + 1/2 a t²
" s "is distance
" u " is initial velocity
" t " is time taken
" a " acceleration
Now, According to Question
For body 1,
u = 0
acceleration ( gravity)
= a ( g )
Distance = s₁ = h
Time taken to reach the ground = t₁
As we know ,
↠ s₁ = u t₁ + 1/2 a t₁²
❥ ( h ) = ( 0 ) t₁ + (1/2) (g) t₁²
❥ h = g t₁²/2
❥ g = 2 h / t₁² .........(1)
For body 2,
u = 0
a = g
distance ↠ s₂ = 4 h
Time taken to reach the ground = t₂
Again according to second law of motion
↠ s₂ = u t₂ + 1/2 a t₂²
❥ ( 4 h ) = ( 0 ) t₂ + ( 1/2 ) ( g ) t₂²
❥ 4 h = g t₂² / 2
❥ g = 8 h / t₂² . .......... (2)
From (1) & (2) we get
❥ 2 h / t₁² = 8 h / t₂²
❥. t₁² / t₂² = (2 h) / (8 h)
❥ t₁² / t₂² = 1 / 4
❥ t₁ / t₂ = 1 / 2
Hence ,
Ratio of the time taken by the bodies is.
t₁ : t₂ ↠ 1 : 2
Option B is correct.
More to know :-)
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❥ Free fall means that an object is falling freely with no forces acting upon it except gravity, a defined constant, g = -9.8 m/s2. The distance the object falls, or height, h, is 1/2 gravity x the square of the time falling. Velocity is defined as gravity x time.
❥ An object that falls through a vacuum is subjected to only one external force, the gravitational force, expressed as the weight of the object. An object that is moving only because of the action of gravity is said to be free falling and its motion is described by Newton's second law of motion.
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