Question

Following table gives the values of weight of a body of mass 25 kg on different surfaces. Observe the values and answer the questions that follow.
Name of place Value of weight
Earth’s equator 245 N
Centre of earth 0 N
Surface of Sun 6850 N
Jupiter 612.5 N
Moon 40.8 N
(a) What is the ratio of ‘g’ on earth and on Jupiter?
(b) How is the value of ‘G’ on sun different from the value of ‘G’on moon? Why?
(c) On what factors does weight of a body on a particular surface depend?
(d)Why is the weight zero at the centerof earth? What is this state called?
(e) If radius of Jupiter is about 10 times of radiusof Earth, find the mass of Jupiter in terms of mass of Earth.

Answer 1

Answer:

a=5:2

b. G(it gives gravitational constant)

so,it is not different on different places

c. radius

d. because force of attraction is equal and balanced at centre of the earth.

e. 25 times of the earth

Answer 2

Answer:

(a) The ratio of ‘g’ on earth and on Jupiter is 0.40.

(b) The value of 'G' remains constant irrespective of the surface.

(c) The weight of a body depends on mass and acceleration due to gravity.

(d) The weight is zero at the center of the earth as acceleration due to gravity is zero at the center. This state is called the state of weightlessness.

(e)The mass of Jupiter is 100 times the mass of Earth.

Explanation:

Weight is defined as the measure of the amount of force acting on a mass due to gravity.

(a)

Weight of the body on jupiter=612.5N    (1)

And we know,

Weight of a body = mass(M)×acceleration due to gravity(g) (2)

So, from equations (1) and (2) we get;

612.5=25×gj

Mass of the body= 25 kg (given)

gj= acceleration due to gravity on the surface of Jupiter

$g_j=\frac{612.5}{25}=24.5$             (3)

acceleration due to gravity on the surface of the earth(ge)=10 ms⁻²

As per the question,

$\frac{g_e}{g_j}=\frac{10}{24.5}=0.40$                 (4)

(b) The value of gravitational constant on the sun and the moon is

6.67×10⁻¹¹ Nm²kg⁻² i.e. irrespective of the location the value of universal gravitational constant "G" remains constant.

(c)The weight of the body depends on mass as well as acceleration due to gravity which varies from place to place.

(d)The weight is zero at the center of the earth as acceleration due to gravity is zero at the center of the earth. And this state is called the state of weightlessness.

The acceleration due to gravity is zero at the center of the earth because at the center we are surrounded by equal masses in all the directions, and equivalent gravitational force acting on us due to earth is zero and thus making acceleration due to gravity zero.

(e)

As per the question,

Rj=radius of jupiter=10Re

Re=radius of earth

And acceleration due to gravity(g) is given as;

$g=\frac{GM}{R^2}$            (5)

G=universal gravitational constant

M=mass of the planet

R=radius of the planet

By using equation (5) we get;

$\frac{GM_j}{(10R_e)^2}=\frac{GM_e}{R_e^2}$          (6)

Where,

Mj=mass of Jupiter

Me=mass of Earth

So we get,

$M_j=100M_e$

The mass of Jupiter will be 100 times the mass of Earth.

Hence, The ratio of ‘g’ on earth and on Jupiter is 0.40, the value of 'G' remains constant irrespective of the surface, The weight of the body depends on its mass and acceleration due to gravity, The weight is zero at the center of the earth as acceleration due to gravity is zero at the center of the earth. And this state is called the state of weightlessness., The mass of Jupiter is 100 times the mass of Earth.