MISSION 35

Ans. Newton

Ans. Area

Ans. Radius

Ans. GMm / R²

Ans. increases

Ans. 6

Ans. Greater

Ans. Kg

Ans. Four times

Ans.
SI Unit: Nm²/kg²
CGS Unit: Dyne

Ans.
Gravitational force

Ans. Gravitational force

Ans.
This is because of the velocity of the moon and the satellites along their orbits. If this velocity was not there, they would have fallen on the earth.

Ans.
1. Though the spacecraft is at a height from the surface of the earth, the value of g there is not zero. In the space station the value of g is only 11% less than its value on the surface of the earth. Thus, the height of a spacecraft is not the reason for their weightlessness.
2. Their weightlessness is caused by their being in the state of free fall. Though the spacecraft is not falling on the earth because of its velocity along the orbit, the only force acting on it is the gravitational force of the earth and therefore it is in a free fall.
3. As the velocity of free fall does not depend on the properties of an object, the velocity of free fall is the same for the spacecraft, the travelers and the objects in the craft.
4. Thus, if a traveler releases an object from her hand, it will remain stationary with respect to her and will appear to be weightless.

Ans.
1. The level of sea water at any given location along sea shore increases and decreases twice a day at regular intervals. High and low tides occur at different times at different places.
2. The level of water in the sea changes because of the gravitational force exerted by the moon. Water directly under the moon gets pulled towards the moon and the level of water there goes up causing high tide at that place.
3. At two places on the earth at 90 degrees from the place of high tide, the level of water is minimum and low tides occur there.

Ans.
1. Mass is a fundamental quantity whose value remains the same everywhere. Hence the mass of an object will not change from place to place.
2. Weight of an object is the product of mass and gravitational acceleration, i.e. W = F = mg
3. As the weight depends on the value of acceleration due to gravity (g) which changes from place to place, the weight of an object changes from place to place though its mass is constant.

Ans.
1. The motion of a body falling in air is accelerated due to the earth's gravitational force on the body. The force due to buoyancy of air acts on the body in the upward direction. As the body falls, the friction with air opposes its motion.
2. This opposition due to air depends on the size, shape, density and velocity of the body. It is greater for a feather than for a stone. Hence, the stone has greater downward acceleration than the feather. Therefore, the stone reaches the ground earlier than the feather though they are released simultaneously from the same height.

Ans.
Variation in value of "g"
1. Change along the surface of the earth :
   The shape of the earth is not exactly spherical and so the distance of a point on the surface of the earth from its center differs somewhat from place to place. Due to its rotation, the earth bulges at the equator and is flatter at the poles. Its radius is largest at the equator and smallest at the poles. The value of g is thus highest (9.832 m/s2) at the poles and decreases slowly with decreasing latitude. It is lowest(9.78 m/s2) at the equator.
2. Change with height :
   As we go above the earth's surface, the value of r increases and the value of g decreases. However, the decrease is rather small for heights which are small in comparison to the earth's radius. For example, remember that the radius of the earth is 6400 km. If an aero plane is flying at a height 10 km above the surface of the earth, its distance from the earth's surface changes from 6400 km to 6410 km and the change in the value of g due to it is negligible. On the other hand, when we consider an artificial satellite orbiting the earth, we have to take into account the change in the value of g due to the large change in the distance of the satellite from the center of the earth. Some typical heights and the values of g at these heights are given in the following table.
3. Change with depth :
   The value of g also changes if we go inside the earth. The value of r decreases and one would think that the value of g should increase as per the formula. However, the part of the earth which contributes towards the gravitational force felt by the object also decreases. Which means that the value of M also decreases. As a combined result of change in r and M, the value of g decreases as we go deep inside the earth.

Ans.
The value of 'g' would be 8 times of what it is now.

The value of 'g' at the center of the earth will be 0.

Ans.
1. It'll be one-fourth of your weight on the surface on the earth.
2. Explanation :
   Weight, W = GMm/R² = GMm/2R² = GMm/4R²
3. As the weight depends on the value of acceleration due to gravity (g) which changes from place to place, the weight of an object changes from place to place though its mass is constant.

Ans.
• Let the mass of the heavy object be m. Thus, the weight of the object or the pull of the floor on the object is W=mg
• Now, if g becomes twice, then the weight of the object or the pull of the floor on the object also becomes twice i.e. W'=2mg=2W
• Thus, because of doubling of the pull on the object due to the floor, it will become two times more difficult to pull it along the floor.