# National Science Olympiad Model Paper 1 Questions and Answers Part 1

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Q. 1. Statement: The universal gravitational constant is same as acceleration due to gravity.

Reason: Gravitational constant and acceleration due to gravity have same dimensional formula.

(A) Both statement and reason are true, and the reason is the correct explanation of the statement.

(B) If both statement and reason are true but reason is not the correct explanation of the statement.

(C) Statement is true, but reason is false.

(D) Statement and reason both are false.

Answer: D

Explanation:

The universal gravitational constant G is totally different from g.

The constant G is scalar and possess the dimensions

g is a vector and has got the dimensions

It is not a universal constant.

Q. 2. Assuming the earth to have a constant density, point out which of the following curves show the variation of acceleration due to gravity from the center of earth to the points far away from the surface of earth.

(A)

(B)

(C)

(D) None of these

Answer: C

Explanation:

And (if r > R)

so, option could be C.

Q. 3. The given figure shows the motion of a planet around the sun in an elliptical orbit with sun at the focus. The shaded areas A and B are also shown in the figure which can be assumed to be equal. If and represent the time for the planet to move from a to b and d to c respectively, then

(A)

(B)

(C)

(D)

Answer: C

Areal velocity of the planet remains constant. If the areas A and B are equal, then .

Kepler՚s second law of area: A radius vector joining any planet to the Sun sweeps out equal area in equal length of time.

By second law, area swept is same and hence time is same i.e.. .

Q. 4. Two satellites having masses of and are revolving the earth in circular orbits of radius _{} and () respectively. Which of the following statement is true regarding their velocities and ?

(A)

(B)

(C)

(D)

Answer: B

Explanation:

We know that from Kepler՚s law Velocity,

, where M is mass of the earth.

So, For satellite 1

For satellite 2

It is given that so,

5. A body weighs 700 gm on the surface of the earth. How much will it weigh on the surface of a planet whose mass is and radius is half that of the earth.

(A) 400 gm

(B) 500 gm

(C) 100 gm

(D) 350 gm

Answer: A

Explanation:

We know that,

On the planet,

Hence weight on the planet,