Question:
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.
Answer:
Let us assume both stones meet at time 't'.
Height of the tower (h) = 100m
Stone 1 dropped from the top of a tower: initial velocity of the stone (u) = 0 m/s
acceleration due to gravity (g) is +ve = +9.8 m/s
2 At time t, it will cover distance (h
1), then using equation S = ut + ½at
2 ⇒ h
1 = 0 + ½gt
2 = (½)(9.8)t
2 = 4.9t
2 
Stone 2 thrown upwards: initial velocity (u) = 25 m/s
acceleration due to gravity (g) is negative = - 9.8 m/s
2 At time t, 2nd stone reaches height (h
2), then using equation S = ut + ½at
2 ⇒ h
2 = 25t - ½gt
2 = 25t - (½)(9.8)t
2 = 25t - 4.9t
2
Because Total height h = 100 m = h
1 + h
2 ⇒
4.9t2 + 25t - 4.9t2 = 100
⇒ 25t - 100
⇒ t = 4s.
In 4 seconds, both stones will meet.
h1 (height from top) = 4.9 × 16 = 78.4m or 100- 78.4 = 21.6m from ground.
Both stones will meet at 21.6 m from ground.
(Note: If you take g = 10 m/s2 , the height will come as 20m)
Gravitation
Q 1.
State Kepler’s Laws of planetary motion. How did Newton guess inverse square law ?
Q 2.
Calculate the value of acceleration due to gravity on Moon. Given mass of Moon =
kg, radius of Moon = 1740 km
Q 3.
A particle is dropped from a tower 180 m high.How long does it take to reach the ground ? What is the velocity when it touches the ground ? Take g =
Q 4.
Why do sewing needles and all pins have a sharp pointed tip?
Q 5.
What is the value of ‘g’ at the centre of Earth ?
Q 6.
Fill in the blanks :
Every object in the universe ________ other bodies.
Q 7.
What do you mean by acceleration due to gravity ?
Q 8.
A boy on a clif£ 49 m high drops a stone.One second later,he throws a second stone after the first.They both hit the ground at the same time. With what speed did he throw the second stone ?
Q 9.
Which force is responsible for tides in the ocean at night ?
Q 10.
Fill in the blanks :
________ of an object is the force of gravity acting on it.
Q 11.
Can you calculate density of Earth from Newton’s law of gravitation ?
Q 12.
What do we call the gravitational force between the Earth and an object ?
Q 13.
Two stones A and B are dropped from a multistoried building. A is dropped from 100 m and after some time B is dropped from 50 m height. Both of them reach the earth at the same time. Will they have equal velocity while reaching the ground ? Calculate and find out the answer (take g =10 m/s
2).
Q 14.
Suppose a planet exists whose mass and radius both,are half those of Earth.Calculate the acceleration due to gravity on the surface of this planet.
Q 15.
State and explain universal law of gravitation given by Newton.What is the importance of this law
Q 16.
The mass of Earth is
kg and that of moon is
kg. If the distance between the Earth and the Moon is
km, calculate the force exerted by Earth on the Moon. Given G =
.
Q 17.
Who measured the value of G first time, experimentally?
Q 18.
At what height above the surface of the earth, the value of 'g' becomes 64% of its value at the surface of the earth. Take radius of the earth = 6400 km.
Q 19.
Calculate the force of gravitation between two objects of masses 80 kg and 1200 kg kept at a distance of 10 m from eachother.Given, G =
/
.
Q 20.
Fill in the blanks :
Assuming negligible air drag, if a steel ball and a table tennis ball are dropped from a height of 100 metres, both will reach the ground at ________ time(s). (same/different)
Q 21.
What is the importance of universal law of gravitation ?
Q 22.
What happens to 'g' experienced by a body when it moves up the earth's surface?
Q 23.
Gravitational force acts on all objects in proportion to their masses.Why then,a heavy object does not fall faster than a light object ?
Q 24.
What is the gravitational acceleration of a spaceship at a distance equal to two Earth’s radius from the centre of the Earth ?
Q 25.
Fill in the blanks :
Heliocentric model was proposed by ______.
Q 26.
Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth = 6 × 10
24 kg and of the Sun = 2 × 10
30 kg. The average distance between the two is 1.5 × 10
11 m.
Q 27.
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
Q 29.
Then why Is the Earth not seen moving towards the stone ?
Q 30.
Write the standard equations of motion when an object is thrown upwards with some initial velocity?
Q 32.
Is weight a scalar quantity?
Q 33.
What is value of ‘g’ on Earth ?
Q 34.
What was geocentric model? Who proposed this theory?
Q 35.
A stone drops from the edge of the roof.It passes a window 2 m high in 0.1 s.How far is the roof above the top of the window
Q 36.
Can a body have weight but no mass ?
Q 37.
Fill in the blanks :
The value of
g on the earth's surface is ______.
Q 38.
Why is the weight of an object on the moon 1/6th its weight on the earth?
Q 39.
What do you mean by Thrust or Buoyant force?
Q 40.
What are Plimsoll Lines?
Q 41.
How does the force of gravitation between two objects change when the distance between them is reduced to half ?
Q 42.
State and explain universal law of gravitation.What is its importance ?
Q 43.
Write down the equations of motion of objects under the influence of gravitational force of Earth.Explain the meaning of the symbols used.
Q 44.
Fill in the blanks :
When objects of different masses and sizes are dropped from same height would reach the ground at ______ (same time/different times), considering negligible air resistance.
Q 45.
Why is G called the Universal Constant?
Q 46.
Mass of an object is 10 kg. What is its weight on the Earth? (g = 9.8 m/s
2.)
Q 47.
Fill in the blanks :
All other variables remaining constant, the force of gravitation is ________ proportional to the square of distance between the two objects.
Q 48.
What are the factors the buoyant force depends on?
Q 49.
The gravitational force between two objects is 100 N. How should the distance between these objects be changed so that force between them becomes 50 N ?
Q 50.
A car falls off a ledge and drops to the ground in 0.5 s.Let g =
(for simplifying the calculations).
(i) What is its speed on striking the ground ?
(ii) What is its average speed during 0.5 s ?
(iii) How high is the ledge from the ground ?
