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 force of gravitation between the Earth and the Sun,given that the mass of the Earth =
kg and mass of the Sun =
kg. The average distance between the two is
m.
Q 3.
Can you calculate density of Earth from Newton’s law of gravitation ?
Q 4.
What do we call the gravitational force between the Earth and an object ?
Q 5.
What is the value of ‘g’ at the centre of Earth ?
Q 6.
What do you mean by acceleration due to gravity ?
Q 7.
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 8.
Why do sewing needles and all pins have a sharp pointed tip?
Q 9.
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 10.
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 11.
Fill in the blanks :
Weight of an object is the product of ______ and ________.
Q 12.
Fill in the blanks :
Every object in the universe ________ other bodies.
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.
Calculate the value of acceleration due to gravity on Moon. Given mass of Moon =
kg, radius of Moon = 1740 km
Q 15.
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 16.
Is weight a scalar quantity?
Q 17.
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 18.
Fill in the blanks :
________ of an object is the force of gravity acting on it.
Q 19.
Fill in the blanks :
The gravitational force between the earth and the object is generally called ____________.
Q 20.
The volume of a 500 g sealed packet is 350 cm
3. Will the packet float or sink in water if the density of water is 1 g cm
-3? What will be the mass of the water displaced by this packet?
Q 21.
In Fig.,the line that joins a planet to the sun sweeps out areas
,
in time intervals 6 weeks,3 weeks and 2 weeks respectively.How are
,
realted ?
Q 22.
Fill in the blanks :
Heliocentric model was proposed by ______.
Q 23.
What are the Kepler Laws that govern the motion of the planets?
Q 24.
Define weight? How it is related to mass?
Q 25.
Mass of an object is 10 kg. What is its weight on the Earth? (g = 9.8 m/s
2.)
Q 27.
Is mass a scalar quantity?
Q 29.
Fill in the blanks :
The SI unit of mass is ______.
Q 30.
Fill in the blanks :
It is the ____________ of the earth, which holds our atmosphere in place.
Q 31.
Why does an object float or sink when placed on the surface of the water?
Q 32.
Why will a sheet of paper fall slower than one that is crumpled into a ball?
Q 33.
The volume of 50 g of a substance is 20 cm
3. If the density of water is 1 g cm
-3, will the substance float or sink?
Q 34.
As you climb up a mountain, your ears “pop” because of the changes in atmospheric pressure. In which direction, outward or inward, does your eardrum move when you climb up?
Q 35.
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 36.
What is the gravitational acceleration of a spaceship at a distance equal to two Earth’s radius from the centre of the Earth ?
Q 37.
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 38.
Mass of an object is 10 kg. What is its weight on Earth ?
Q 39.
A ball is thrown up with a speed of 15 m/s.How high will it go before it begins to fall ? Take g=
Q 40.
How does the force of gravitation between two objects change when the distance between them is reduced to half ?
Q 41.
What is the magnitude of the gravitational force between the Earth and a 1 kg on its surface ? (Mass of the Earth Is
kg and radius of the Earth is
m.)
Q 42.
Two objects of masses
having the same size are dropped simultaneously from heights
respectively.Find out the ratio of time they would take in reaching the ground.Will this ratio remain the same if (1) one of the objects is hollow and the other one is solid and (ii) both of them are hollow,size remaining the same in each case.Give reason.
Q 43.
The distance between two objects is doubled. What happens to gravitational force between them
Q 44.
Who explained the motion of planets around the Sun ?
Q 45.
What is the usual shape of orbits of planets around the Sun ?
Q 46.
A stone falling towards Earth also attracts the Earth with the same force.Is it true ?
Q 47.
A body is projected upwards. What is its velocity at maximum height
Q 48.
What is the weight of a body of mass 1 kg on Earth ?
Q 49.
What is inverse square rule ?
Q 50.
Can a body have weight but no mass ?
