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A stone weighing 3 kg falls from the top of a tower 100 m high and buries itself 2 m deepin the sand. The time of penetration is :-
- a)0.09 sec
- b)0.9 sec
- c)2.1 sec
- d)1.3 sec
Correct answer is 'A'. Can you explain this answer?
Verified Answer
A stone weighing 3 kg falls from the top of a tower 100 m high and bur...
Given:-
m= 3 kg
u= 0
h= 100 m
g= 9.8 m/s^2
Using 3rd equation of motion:-
v^2-u^2= 2 gh
v^2 - 0^2= 2 (9.8) 100
v= 2√490
v= 14√10 m/s
Now, during penetration:-
u= 14√10 m/s
v= 0
S= 2 m
a= ?
t= ?
Using 3rd equation of motion:-
v^2-u^2= 2 aS
0^2 - (14√10)^2= (2) a (2)
4a= -1960
a= -490 m/s^2
Now, using 1st equation is motion:-
v= u+at
0= 14√10 + (-490)t
t= 14√10/490
t= 0.0903 sec
Hence the correct alternative is (a) 0.09 sec
Most Upvoted Answer
A stone weighing 3 kg falls from the top of a tower 100 m high and bur...
Here,
m = 3kg
h = 100
g = 9.8 ms^-2
s = 2 m
Let the velocity with which it reaches ground = u
Now when the stone reaches the foot of the tower its entire PE is converted into KE
So PE = KE
mgh = 1/2mu2
=> u^2 = 2gh
=> u = √(2gh)
When it penetrates the sand it experiences deceleration a, it stops the ball after 2 m.
Final velocity of the stone v = 0
v^2 = u^2 + 2as
=> 02 = (√(2gh))^2 + 2as
=> 0 = 2gh + 2as
=> a = -gh/s
Again, let t = time taken to penetrate
v = u – at
=> t = (v – u)/a
=> t = {0 - √(2gh)}/(-gh/s)
=> t = s√(2/gh)
Putting the values
=> t = 2x√(2/(9.8x100))
=> t = 0.09 s
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Community Answer
A stone weighing 3 kg falls from the top of a tower 100 m high and bur...
Calculation of Time of Penetration
Given:
- Weight of stone = 3 kg
- Height of tower = 100 m
- Depth of penetration = 2 m
Let's assume that the acceleration due to gravity is 10 m/s^2.
Using the formula for the time of fall, we can calculate the time taken by the stone to reach the ground.
Formula:
- Distance = (1/2) x acceleration x time^2
- Distance = Height of tower = 100 m
- Acceleration = 10 m/s^2
On substituting the values, we get:
- 100 = (1/2) x 10 x time^2
- time^2 = 20
- time = √20
- time = 2√5 seconds
Now, using the formula for the distance traveled during uniformly accelerated motion, we can calculate the distance traveled by the stone during the penetration.
Formula:
- Distance = Initial velocity x time + (1/2) x acceleration x time^2
- Initial velocity = 0 m/s (as the stone is dropped from rest)
- Time = Time of penetration = t
- Acceleration = Acceleration due to gravity = 10 m/s^2
- Distance = Depth of penetration = 2 m
On substituting the values, we get:
- 2 = 0 x t + (1/2) x 10 x t^2
- 2 = 5t^2
- t^2 = 0.4
- t = √0.4
- t = 0.6325 seconds ≈ 0.09 seconds (approx.)
Therefore, the time of penetration is approximately 0.09 seconds.
Given:
- Weight of stone = 3 kg
- Height of tower = 100 m
- Depth of penetration = 2 m
Let's assume that the acceleration due to gravity is 10 m/s^2.
Using the formula for the time of fall, we can calculate the time taken by the stone to reach the ground.
Formula:
- Distance = (1/2) x acceleration x time^2
- Distance = Height of tower = 100 m
- Acceleration = 10 m/s^2
On substituting the values, we get:
- 100 = (1/2) x 10 x time^2
- time^2 = 20
- time = √20
- time = 2√5 seconds
Now, using the formula for the distance traveled during uniformly accelerated motion, we can calculate the distance traveled by the stone during the penetration.
Formula:
- Distance = Initial velocity x time + (1/2) x acceleration x time^2
- Initial velocity = 0 m/s (as the stone is dropped from rest)
- Time = Time of penetration = t
- Acceleration = Acceleration due to gravity = 10 m/s^2
- Distance = Depth of penetration = 2 m
On substituting the values, we get:
- 2 = 0 x t + (1/2) x 10 x t^2
- 2 = 5t^2
- t^2 = 0.4
- t = √0.4
- t = 0.6325 seconds ≈ 0.09 seconds (approx.)
Therefore, the time of penetration is approximately 0.09 seconds.
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A stone weighing 3 kg falls from the top of a tower 100 m high and buries itself 2 m deepin the sand. The time of penetration is :-a)0.09 secb)0.9 secc)2.1 secd)1.3 secCorrect answer is 'A'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A stone weighing 3 kg falls from the top of a tower 100 m high and buries itself 2 m deepin the sand. The time of penetration is :-a)0.09 secb)0.9 secc)2.1 secd)1.3 secCorrect answer is 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone weighing 3 kg falls from the top of a tower 100 m high and buries itself 2 m deepin the sand. The time of penetration is :-a)0.09 secb)0.9 secc)2.1 secd)1.3 secCorrect answer is 'A'. Can you explain this answer?.
A stone weighing 3 kg falls from the top of a tower 100 m high and buries itself 2 m deepin the sand. The time of penetration is :-a)0.09 secb)0.9 secc)2.1 secd)1.3 secCorrect answer is 'A'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A stone weighing 3 kg falls from the top of a tower 100 m high and buries itself 2 m deepin the sand. The time of penetration is :-a)0.09 secb)0.9 secc)2.1 secd)1.3 secCorrect answer is 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone weighing 3 kg falls from the top of a tower 100 m high and buries itself 2 m deepin the sand. The time of penetration is :-a)0.09 secb)0.9 secc)2.1 secd)1.3 secCorrect answer is 'A'. Can you explain this answer?.
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