# Question-1

**Which of the following symptoms is likely to afflict an astronaut in space (a) swollen feet, (b) swollen face (c) headache (d) orientational problem.**

**Solution:**

An astronaut in space is most likely to be afflicted by the following 3 problems:

(a) swollen face, (b) headache and (c) orientational problem.

# Question-2

**A person in an artificial satellite of earth feels weightlessness. But a person the moon has weight though the moon is also a satellite of the earth. Why?**

**Solution:**

The gravitational force of attraction of the earth on the person inside the satellite provides the necessary centripetal force to move in an orbit on the other hand, the person has weight on the moon due to the additional gravitational pull of the moon.

# Question-3

Why springs are made of steel and not of copper?

This is bacause steel is more elastic than copper. The value of Young's modulus for steel is 2.0*10

**Solution:**

This is bacause steel is more elastic than copper. The value of Young's modulus for steel is 2.0*10

^{11}pa.The value of Y for copper is 1.1*10

^{11}.

# Question-4

**What would be the speed of rotation of the Earth in order that a body on the equator has no weight? Determine the apparent weights of the bodies situated at a latitude of 60**

**Â°**

**and at the poles. The radius of the Earth = 6400 km and**

g = 9.8 m/s

g = 9.8 m/s

^{2}.**Solution:**

The body will become weightless if the gravitational force mg on it is entirely used up in providing the centripetal acceleration for the rotation of the Earth.

or Ï‰ = 1.237 Ã— 10

^{-3}rad/s

The bodies on the equator will have no weight if the Earth rotates at this speed. At a latitude Ï† , the apparent weight Wâ€² is given by,

Wâ€² = mg

But g = Ï‰

^{2}R

âˆ´ Wâ€² = mg (1 â€“ cos

^{2}Ï† )

But cos Ï† = cos 60Â° =

âˆ´ Wâ€² = mg

At the poles, Ï† = Ï€ /2

âˆ´ Wâ€² = mg = true weight.

# Question-5

**The change in the value of g at a height â€˜hâ€™ above the Earth is same as at a depth â€˜dâ€™ below it. If h and d are small when compared to the radius of the Earth, what is the ratio (h/d)?**

**Solution:**

# Question-6

**The radius of the Earth is reduced by 4%. The mass of earth remains unchanged. What will be the change in escape velocity?**

**Solution:**

Escape velocity, say V, is given by

Thus, the decrease in the radius by 4% will increase the escape velocity by 2%.

# Question-7

**The mass and diameter of a planet are twice those of the Earth. What will be the period of oscillation of a pendulum on this planet, if it is a secondâ€™s pendulum on the Earth?**

**Solution:**

We know, g =

âˆ´ g

_{e}= and g

_{p}=

Mass of the planet M

_{p}= 2 M

_{e}

Radius of the planet R

_{p}= 2R

_{e}

âˆ´

The time period of a simple pendulum is given by

T

_{e}= 2Ï€

and T

_{p}= 2Ï€

âˆ´

or .

# Question-8

**If the Earth rotates fast enough, so that the apparent weight of the body at the equator is zero, what will be the angular velocity of the Earth and duration of the day? Take the radius of the Earth, R = 6400km.**

**Solution:**

# Question-9

**If the Earth were to cease rotating about its own axis, what would be the change in the values at a place of latitude 45**

**Â° . Assume the Earth to be a sphere of radius 6.38 Ã—**

**10**

^{3}km.**Solution:**

We know,

Given: Î» = 45Â°

cos^{2} Î» = (1/2)

Substituting the values, we get

.

# Question-10

**Suppose a hole were drilled completely through the Earth along a diameter. Show that the force on a mass m at a distance r from the centre of the Earth is F = .**

**Solution:**

The gravitational force on the mass m arises only from a sphere of radius r enclosing the mass as shown in the fig.

Mass of the sphere, , where r is the density of the Earth.

The force on the mass m is

-ve sign indicates that the force is attractive.

, where M is the total mass of the Earth.

Moreover, acceleration acting along the mass m is given by,

It proves that m will execute S.H.M. about the centre of the Earth O.

# Question-11

**If the kinetic energy of a satellite revolving in an orbit close to the earth happens to be doubled, will the satellite escape?**

**Solution:**

It will escape because its velocity will become equal to the escape velocity.

# Question-12

**The tidal effect of the moonâ€™s pull is greater than the tidal effect of the sun although the sunâ€™s pull is greater than moonâ€™s pull. Explain why?**

**Solution:**

Tidal effect depends inversely on the cube of the distance unlike gravitational force, which depends inversely on the square of the distance.

# Question-13

**How will the value of acceleration due to gravity be affected if the earth begins to rotate at a speed greater than its present speed?**

**Solution:**

Acceleration due to gravity due to the earth is given by

when Ï‰ increases, gâ€² will decrease.

# Question-14

**If the earth stops rotating about its axis by what value will the acceleration due to gravity at equator change?**

**Solution:**

The acceleration due to gravity at equator will increase by R Ï‰

^{2}where R is the radius of earth and Ï‰ is the angular velocity of rotation of earth.

# Question-15

**Where is the gravitational field zero and where is the gravitational potential zero, in case of earth?**

**Solution:**

Gravitational field is zero at the center of earth and infinity. Gravitational potential is zero at infinity.

# Question-16

**An astronaut, while revolving in a circular orbit happens to throw a ball outside, will the ball reach the surface of earth?**

**Solution:**

The ball will never reach the surface of earth and it will continue to move in the same circular orbit and will chase the astronaut.

# Question-17

**Does a rocket really need the escape velocity of 11.2 km/s initially to escape from the earth?**

**Solution:**

No, a rocket can have any initial velocity at the start but its velocity should continue to increase. It will escape from the earth only if its velocity becomes 11.2 km/s.

# Question-18

**A planet revolves in an elliptical orbit around the sun. The semi major and semi minor axis are a and b. How is time â€“ period related with them?**

**Solution:**

T

^{2}Î± a

^{3}.

# Question-19

**Imagine a spacecraft going from the earth to the moon. How does the weight vary as it goes from the moon?**

**Solution:**

As the spacecraft moves from the surface of the earth towards the moon,

(i) Its weight will start decreasing

(ii) It becomes zero at the point where the forces of attraction on the spacecraft due to the earth and

moon will just become equal and opposite

(iii) It will again start increasing as the spacecraft further moves towards the moon.