###### Advertisements

###### Advertisements

The radius of a circle is stated as 2.12 cm. Its area should be written as

#### Options

14 cm

^{2}14.1 cm

^{2}14.11 cm

^{2}14.1124 cm

^{2}

###### Advertisements

#### Solution

14.1 cm^{2}

Area of a circle, A= \[\pi r^2\] On putting the values, we get:

\[A = \frac{22}{7} \times 2 . 12 \times 2 . 12\]

\[ \Rightarrow A = 14 . 1 {cm}^2\]

The rules to determine the number of significant digits says that in the multiplication of two or more numbers, the number of significant digits in the answer should be equal to that of the number with the minimum number of significant digits. Here, 2.12 cm has a minimum of three significant digits. So, the answer must be written in three significant digits.

#### APPEARS IN

#### RELATED QUESTIONS

India has had a long and unbroken tradition of great scholarship — in mathematics, astronomy, linguistics, logic and ethics. Yet, in parallel with this, several superstitious and obscurantistic attitudes and practices flourished in our society and unfortunately continue even today — among many educated people too. How will you use your knowledge of science to develop strategies to counter these attitudes ?

What are the dimensions of volume of a sphere of radius *a?*

What are the dimensions of the ratio of the volume of a cube of edge *a* to the volume of a sphere of radius *a*?

If two quantities have same dimensions, do they represent same physical content?

Find the dimensions of linear momentum .

Find the dimensions of pressure.

Find the dimensions of the specific heat capacity c.

(a) the specific heat capacity c,

(b) the coefficient of linear expansion α and

(c) the gas constant R.

Some of the equations involving these quantities are \[Q = mc\left( T_2 - T_1 \right), l_t = l_0 \left[ 1 + \alpha\left( T_2 - T_1 \right) \right]\] and PV = nRT.

The height of mercury column in a barometer in a Calcutta laboratory was recorded to be 75 cm. Calculate this pressure in SI and CGS units using the following data : Specific gravity of mercury = \[13 \cdot 6\] , Density of \[\text{ water} = {10}^3 kg/ m^3 , g = 9 \cdot 8 m/ s^2\] at Calcutta. Pressure

= hpg in usual symbols.

Test if the following equation is dimensionally correct:

\[h = \frac{2S cos\theta}{\text{ prg }},\]

where h = height, S = surface tension, ρ = density, I = moment of interia.

Test if the following equation is dimensionally correct:

\[V = \frac{\pi P r^4 t}{8 \eta l}\]

where v = frequency, P = pressure, η = coefficient of viscosity.

Can you add three unit vectors to get a unit vector? Does your answer change if two unit vectors are along the coordinate axes?

Is the vector sum of the unit vectors \[\vec{i}\] and \[\vec{i}\] a unit vector? If no, can you multiply this sum by a scalar number to get a unit vector?

The magnitude of the vector product of two vectors \[\left| \vec{A} \right|\] and \[\left| \vec{B} \right|\] may be

(a) greater than AB

(b) equal to AB

(c) less than AB

(d) equal to zero.

A vector \[\vec{A}\] makes an angle of 20° and \[\vec{B}\] makes an angle of 110° with the X-axis. The magnitudes of these vectors are 3 m and 4 m respectively. Find the resultant.

Add vectors \[\vec{A} , \vec{B} \text { and } \vec{C}\] each having magnitude of 100 unit and inclined to the X-axis at angles 45°, 135° and 315° respectively.

Two vectors have magnitudes 2 unit and 4 unit respectively. What should be the angle between them if the magnitude of the resultant is (a) 1 unit, (b) 5 unit and (c) 7 unit.

Let \[\vec{a} = 2 \vec{i} + 3 \vec{j} + 4 \vec{k} \text { and } \vec{b} = 3 \vec{i} + 4 \vec{j} + 5 \vec{k}\] Find the angle between them.

The electric current in a charging R−C circuit is given by i = i_{0}_{ }e^{−t}^{/RC} where i_{0}, R and C are constant parameters of the circuit and t is time. Find the rate of change of current at (a) t = 0, (b) t = RC, (c) t = 10 RC.

The changes in a function* y* and the independent variable *x* are related as

\[\frac{dy}{dx} = x^2\] . Find *y* as a function of* x*.

Round the following numbers to 2 significant digits.

(a) 3472, (b) 84.16. (c)2.55 and (d) 28.5

In a submarine equipped with sonar, the time delay between the generation of a pulse and its echo after reflection from an enemy submarine is observed to be 80 s. If the speed of sound in water is 1460 ms^{-1}. What is the distance of an enemy submarine?

Jupiter is at a distance of 824.7 million km from the Earth. Its angular diameter is measured to be 35.72˝. Calculate the diameter of Jupiter.

If π = 3.14, then the value of π^{2} is ______

High speed moving particles are studied under