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प्रश्न
A stone is thrown vertically upwards with initial velocity u reaches a height ‘h’ before coming down. Show that the time taken to go up is the same as the time taken to come down.
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उत्तर
We have v = u + at ...(1)
and s = ut + `1/2 "at"^2` ...(2)
∴ s = `("v" - "at")"t" + 1/2"at"^2`
= `"vt" - "at"^2+1/2"at"^2`
∴ `"s" = "vt" - 1/2 "at"^2` ...(3)
As the stone moves upward from (A → B) [AB = h]
S = AB = h, t = t1,
a = − g (retardation)
u = u and v = 0
∴ From Eq. (3), h = 0 − `1/2 (-"g")"t"_1^2`
∴ h = `1/2"gt"_1^2` ...(4)
As the stone moves downward from (B → A)
t = t2, u = 0, s = h and a = g
∴ From Eq. (2), h = `1/2"gt"_2^2` ...(5)
From Eqs. (4) and (5),
`"t"_1^2 = "t"_2^2`
∴ `"t"_1 = "t"_2` (∵ t1, t2 are positive.)
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संबंधित प्रश्न
A stone is allowed to fall from the top of a tower 100 m high and at the same time another stone is projected vertically upwards from the ground with a velocity of 25 m/s. Calculate when and where the two stones will meet.
State whether the following statement is true or false :
A falling stone also attracts the earth.
Explain what is meant by the equation :
`g= Gxxm/r^2`
where the symbols have their usual meanings.
During a free fall, will heavier objects accelerate more than lighter ones ?
An object thrown vertically upwards reaches a height of 500 m. What was its initial velocity? How long will the object take to come back to the earth? Assume g = 10 m/s2
Solve the problem.
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The total energy of an object falling freely towards the ground ______.
A force of 10 N acts on a body of mass 5 kg. Find the acceleration produced.
A force acts for 10 s on a stationary body of mass 100 kg, after which the force ceases to act. The body moves through a distance of 100 m in the next 5 s. Calculate : The acceleration produced by the force
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(Hint : Acceleration = Slope of the v-t graph)
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The value of gravitational acceleration (g) is ________.
The free fall of an object is possible only in _______.
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Read the given passage carefully and answer the questions.
We know that the force of gravity due to the earth acts on each and every object. When we were holding the stone in our hand, the stone was experiencing this force, but it was balanced by a force that we were applying on it in the opposite direction. As a result, the stone remained at rest. Once we release the stone from our hands, the only force that acts on it is the gravitational force of the earth and the stone falls down under its influence. Whenever an object moves under the influence of the force of gravity alone, it is said to be falling freely. Thus the released stone is in a free fall. In free fall, the initial velocity of the object is zero and goes on increasing due to the acceleration due to the gravity of the earth. During free fall, the frictional force due to air opposes the motion of the object and a buoyant force also acts on the object. Thus, true free fall is possible only in a vacuum.
1) Complete the following statement by choosing the right option.
The stone held in the hand is stable because on it __.
- two unbalanced forces are exerted.
- only the gravitational force of the earth is exerted.
- gravitational force of the earth is not exerted.
- two balanced forces are exerted.
2) Why does free fall not happen on the earth?
3) Why does the velocity of the object increase during the free fall?
4) Which type of force exerts on the object during free fall?
5) Why does free fall happen only in a vacuum?
