# Question-1

**How much would a 70kg man weigh on the moon? What would be his mass on the earth and on the moon? (Acceleration due to gravity on moon=1.63m/s**

^{2}).**Solution:**

First we calculate the weight of the moon.

Mass of the man on moon, m = 70 kg

Acceleration due to gravity, g = 1.63m/s

^{2}

(on the moon)

We know that: W = m x g

So, W = 70 x 1.63

W = 114.1N

Thus the man would weigh 114.1 newtons on the moon. Please note that the mass of a body is constant everywhere in the universe. So, the mass of this man would be the same on the earth as well as on the moon, that is, that mass will be 70kg on the earth as well as on the moon.

# Question-2

**What is the mass of an object whose weight is 49 newtons?**

**Solution:**

Weight, W = 49N

Mass, m = ? (To be calculated) Acceleration due to gravity, g = 9.8m/s

^{2}

Now putting these values in the formula,

W = m x g

We get, 49 = m x 9.8

m==5kg

Thus, the mass of the object is 5 kilograms.

# Question-3

**Define range of a projectile.**

**Solution:**

The maximum horizontal distance travelled by a projectile during its flight is called the range of a projectile.

# Question-4

**A body of weight 600N rests on the floor of a lift. If the lift begins to fall freely under gravity, what is the force with which the body presses on the floor?**

**Solution:**

When the lift is falling freely under gravity, then the body of weight 600N kept in it also falls freely under the action of gravity. In this case the reaction (force) of the floor of the lift, on the body is, zero. So the action (force) of the body on the floor of the lift should also be zero. Thus, the body on the floor of the lift exerts no force when the lift is falling freely under gravity. The body is "weightless" under these conditions.

# Question-5

**State the condition under which a stone attached to a spring balance is said to be weightless.**

**Solution:**

When the spring balance is falling freely along with stone, it shows a zero reading for the weight of stone, that is, the stone is "weightless" in this condition.

# Question-6

**Define a parabola.**

**Solution:**

A falling object having a horizontal velocity also along with the vertical velocity, is called a projectile and it moves in a curved path called parabola.

# Question-7

**How can we conclude that the vertical motion of a projectile is independent of its horizontal motion?**

**Solution:**

In a given time interval, the vertical distance travelled by an object thrown parallel to the surface of earth is the same as that travelled by an object dropped directly from the same height. Thus, the vertical motion of a projectile is independent of its horizontal motion.

# Question-8

**What is the nature of all freely falling objects in vacuum?**

**Solution:**

In vacuum, all the freely falling objects have the same acceleration.

# Question-9

**The earth’s gravitational force causes an acceleration of 5m/s**

^{2}in a 1kg mass somewhere in space. How much will the acceleration of a 3kg mass be at the same place?**Solution:**

The acceleration produced by the gravitational force of earth does not depend on the mass of the object. So, the acceleration produced in the 3kg mass will be the same as that produced in 1kg mass, That is, the acceleration produced will be 5m/s

^{2}.

# Question-10

**Give a note on mass.**

**Solution:**

The mass of a body is the quantity of matter (or material) contained in it. Mass is a scalar quantity and it is measured by an ordinary equal arm balance. The unit of mass is kilogram. A body contains the same quantity of matter wherever it be-whether on the earth, moon or even in outer space. Thus, the mass of a body is constant and does not change from place to place. Mass of a body is usually denoted by the small ‘m’. Mass of a body is a measure of inertia of the body and hence it is also known as inertial mass. The mass of a body cannot be zero.

# Question-11

**What is the equation for the force of gravitation between two particles?**

**Solution:**

A force is acting along the line joining two particles 1 and 2. If particle 1 attracts particle 2 with a force F

_{12}, then particle 2 pulls particle 1 with a force F

_{21}of equal magnitude. Both the forces are along the line joining the particles.

According to Newton’s third law, the force F_{12} is the action and the force F_{21} is the reaction. These forces form a pair of forces, which are equal in magnitude and opposite in direction. Hence the magnitude of the force of gravitation between these two particles of masses m_{1} and m_{2} separated by a distance r is

F ∝

or F = G

where G is a constant of proportionality. It is the universal constant of gravitation.

# Question-12

**How will you arrive at the equation for acceleration due to gravity on earth?**

**Solution:**

From Newton’s second law of motion we know that force is the product of mass and acceleration.

F = ma

If the force due to gravity on a particle of mass m has magnitude

F = mg

where g denotes the acceleration due to gravity, then by using the equation of force of gravitation

F =

we get

mg = G

g = G

where M is the mass of the earth, r is the distance between the particle and the center of the earth.

If the particle is on or near the surface of the earth, then r is taken equal to R, the radius of the earth. Thus for bodies on or near the surface of the earth,

mg = G

g = G.

# Question-13

**What is the ratio of acceleration due to gravity on the earth to moon?**

**Solution:**

Acceleration due to gravity on earth g = G ----(1)

Acceleration due to gravity on moon a = G ----(2)

Therefore dividing equation (2) by (1), we get

# Question-14

**Define center of mass? When is the center of mass considered as center of gravity?**

**Solution:**

A point in a body where the whole mass of the body is assumed to be concentrated, is called center of mass. On the surface of the earth, or near it, where the force of gravity is constant, the center of mass also becomes the point where the force of gravity on the whole of the body is effectively felt. In this case the center of mass is called center of gravity.

# Question-15

**What is a wobble?**

**Solution:**

The technology detecting irregularities in the motion of stars has been advanced to such an extent that even a very small irregularity in the motion of a star can be detected. Such an irregularity is called a wobble. A wobble may also indicate the possibility of a planet going round the star.

# Question-16

**If a ball is thrown horizontally, what is**

(i) the state of motion in that direction and

(ii) the force acting on the ball in the vertical direction?

(i) the state of motion in that direction and

(ii) the force acting on the ball in the vertical direction?

**Solution:**

(i) According to Newton’s first law of motion the ball travels with a uniform velocity in the horizontal direction.

(ii) In the vertical direction, the ball feels the force of gravity and so it is accelerated in the downward direction.

# Question-17

**What happens to the plants in the absence of gravity?**

**Solution:**

In the absence of gravity, the plants are confused and grow randomly. This condition is not healthy for their growth since they cannot get the necessary nutrients.

# Question-18

**The acceleration due to gravity at the surface of the moon is 1.67 ms**

^{-2}. If the radius of the moon is 1.74 × 10^{6}m, find the mass of the moon. Given G = 6.67 × 10^{-11}Nm^{2}kg^{-2}.**Solution:**

Acceleration due to gravity on moon a = 1.67 ms

^{-2}

Radius of the moon R

_{m}= 1.74 × 106 m

Therefore mass of the moon = M

_{m}=

# Question-19

**An astronaut on the moon measures the acceleration due to gravity and finds it to be 1.67 ms**

^{-2}. He knows that the earth is about 80 times more massive than the moon. What is his estimate of the ratio of the radius of the earth to that of the moon?**Solution:**

The accelerations due to gravity on earth and moon are given by

Therefore

= = 3.69.

# Question-20

**Why is the gravitational force of attraction between two bodies of ordinary mass not noticeable in everyday life?**

**Solution:**

It is because of very small value of the gravitation constant G, the gravitational force between bodies of ordinary mass is extremely small. Hence their acceleration is too small to cause any noticeable motion. The only attraction that we notice is the acceleration due to the earth (g) because the earth is very massive.