NCERT Class 11 Physics Chapter 1 Units and Measurements Very Short Answer Type Questions Part 3

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Question 29:

During a total solar eclipse the moon almost entirely covers the sphere of the sun. Write the relation between the distances and sizes of the sun and moon.

Answer:

Key point: In geometry, a solid angle (symbol: or w) is the two-dimensional angle in three-dimensional space that an object subtends at a point. It is a measure of how large the object appears to an observer looking from that point. In the international System of Unit (SI), a solid angle is expressed in a dimensionless unit called a steradian (symbol: sr).

Ch-1 - Question29- Image of Solid Angle

Ch-1 - Question29- Image of Solid Angle

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A small object nearby may subtend the same solid angle as a larger object farther away. For example, although the Moon is much smaller than the Sun, it is also much closer to Earth

Diagram given below shows that moon almost entirely covers the sphere of the sun.

Let the solid angle made by sun and moon is we can write

Ch-1 - Question29- Image of Solid Angle made by sun and Moon

Ch-1 - Question29- Image of Solid Angle Made by Sun and Moon

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(Here, radius of sun and moon represent their sizes respectively)

Question 30:

If the unit of force is , unit of length is and unit of time is , what is the unit of mass in this system of units?

Answer:

First write dimension of each quantity and then relate them.

Force

Substituting values of L and T from Eqs. (ii) and (iii) in Eq. (i), we get

Question 31:

Give an example of

(a) a physical quantity which has a unit but no dimensions.

(b) a physical quantity which has neither unit nor dimensions.

(c) a constant which has a unit.

(d) a constant which has no unit.

Answer:

(a) Angle or solid angle

(b) Relative density etc.

(c) Planck’s constant, universal gravitational constant, etc.

(d) Raynold number

Question 32:

Calculate the length of the arc of a circle of radius which subtends an angle of at the centre.

Answer:

Key concept:

Plane Angle

Ch-1-Question 32-Image of Plane Angle

Ch-1-Question 32-Image of Plane Angle

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According to the problem,

Hence, length of

Rounding off to three significant figures it would be 16.2 cm.

Question 33:

Calculate the solid angle subtended by the periphery of an area of at a point situated symmetrically at a distance of from the area.

Answer:

Solid angle,

Question 34:

The displacement of a progressive wave is represented by , where is distance and t is time. Write the dimensional formula of

(i) and

(ii) .

Answer:

We have to apply principle of homogeneity to solve this problem. Principle of homogeneity state that in a correct equation, the dimensions of each term added or subtracted must be same, i.e., dimensions of LHS and RHS should be equal. According to the problem

Here

Here which peak value of

So, should be dimensionless

(i)

(ii)

Question 35:

Time for oscillations of a pendulum is measured as; ; s. What is the precision in the measurements? What is the accuracy of the measurement?

Answer:

(a) Precision is given by the least count of the instrument.

For oscillations. Precision

For oscillation, precision

(b)

Max. observed error