How does the weight of an object vary with respect to mass and radius of the earth. In a hypothetical case, if the diameter of the earth becomes half of its present value and its mass becomes four times of its present value, then how would the weight of any object on the surface of the earth be affected?
Soln:
Let R and M be the radius and mass of the earth
Then
Weight of the object = M/R2
Original weight W0 = mg = mg M/R2
Hypothetically 4m and R becomes R/2
Then, weight = mG 4M /(R/2) 2
=(16m g) M/R2
= 10xW0
Weight will be 16 times.
24. How does the force of attraction between the two bodies depend upon their masses and distance between them? A student thought that two bricks tied together would fall faster than a single one under the action of gravity. Do you agree with his hypothesis or not? Comment.
Soln:
The hypothesis is incorrect. Force of attraction between two masses separated by distance r is given by Newton law of gravitation where F= Gm1m2/R2 Where G is gravitational force and it is an universal constant.
Gravitational force is directly proportional to the product of the masses of two bodies and inversely proportional to the square of the distance between them.
Bodies thrown from same height fall with same speed irrespective of their mass. This is due to acceleration due to gravity.
g = GM/R2Where M is mass R is radius of the earth
This equation shows that acceleration due to gravity depends on the mass of the earth and radius of the earth. Hence tow brick tied will not fall faster than the single one.
25. Two objects of masses m1 and m2 having the same size are dropped simultaneously from heights h1 and h2 respectively. Find out the ratio of time they would take in reaching the ground. Will this ratio remain the same if (i) 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.
Soln:
h1 =
h2 =
as x = o
As the acceleration remains the same, the ratio between two objects remains the same. In this case, acceleration does not depend upon mass and size.
26. (a) A cube of side 5 cm is immersed in water and then in saturated salt solution. In which case will it experience a greater buoyant force. If each side of the cube is reduced to 4 cm and then immersed in water, what will be the effect on the buoyant force experienced by the cube as compared to the first case for water. Give reason for each case.
(b) A ball weighing 4 kg of density 4000 kg m–3 is completely immersed in water of density 103 kg m–3 Find the force of buoyancy on it. (Given g = 10 m s–2)
Soln:
(i) Buoyant force, F = Vpg
p = Density of water, V = Volume of water displaced by the body
Volume and density of an object decides its Buoyancy. Cube will experience a greater buoyancy in a saturated solution. If the cube is reduced to 4 cm on each side, the volume of cube becomes less as the buoyancy will be reduced as buoyant force is directly proportional to volume.
(ii) The magnitude of the buoyant force given by F = Vpg
where V = Volume of body immersed in water or volume of water displaced, p = Density of liquid.
-3Hence Volume of solid =
=
=
Buoyancy F = Vpg
=
= 10N
Show solutionHide solution
Solution coming soon.