Advertisements
Advertisements
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.
Advertisements
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.)
APPEARS IN
संबंधित प्रश्न
What do you mean by free fall?
Gravitational force acts on all objects in proportion to their masses. Why then, a heavy object does not fall faster than a light object?
What is the acceleration of free fall?
A stone is released from the top of a tower of height 19.6 m. Calculate its final velocity just before touching the ground.
A stone is thrown vertically upward with an initial velocity of 40 m/s. Taking g = 10 m/s2, find the maximum height reached by the stone. What is the net displacement and the total distance covered by the stone?
A ball thrown up vertically returns to the thrower after 6 s. Find
- the velocity with which it was thrown up,
- the maximum height it reaches, and
- its position after 4 s.
What do you mean by the term free fall ?
During a free fall, will heavier objects accelerate more than lighter ones ?
Name the force which stops you falling through the floor.
What would be the value of ‘g’ on the surface of the earth if its mass was twice and its radius half of what it is now?
A force acts for 0.1 s on a body of mass 2.0 kg initially at rest. The force is then withdrawn and the body moves with a velocity of 2 m s-1. Find the magnitude of the force.
Define the term acceleration due to gravity? Write its S.I. unit.
How is the acccelaration due to gravity on the surface of the earth realted to its mass and radius ?
In vacuum, all freely falling objects have the same force. Is it true?
Free fall of an object does not depend on the mass of the object.
Write scientific reason.
When we drop a feather and a stone at the same time from a height the stone reach the earth faster than a feather.
Define acceleration due to gravity.
Write a short note.
Escape Velocity
The mass and weight of an object on earth are 5 kg and 49 N respectively. What will be their values on the moon? Assume that the acceleration due to gravity on the moon is 1/6th of that on the earth.
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?
