Find the area of the sector of a circle of radius \[5\] cm, if the corresponding arc length is \[3.5\] cm.

Home » Find the area of the sector of a circle of radius cm, if the corresponding arc length is cm.

Find the area of the sector of a circle of radius

$5$

cm, if the corresponding arc length is

$3.5$

cm.

Find the area of the sector of a circle of radius

$5$

cm, if the corresponding arc length is

$3.5$

cm.

solution

Given Radius of the circle = r =

$5$

cm

Given Arc length of the sector = l =

$3.5$

cm

Let us consider the central angle (in radians) be

$\theta$

.

As we know that Arc length = Radius × Central angle (in radians)

From Central angle (

$\theta$

)= Arc length / Radius = l / r =

$3.5/5$

=

$0.7$

radians

As we know that the Area of the sector =

$(1/2)\times {{r}^{2}}\theta$

=

$(1/2)\times 25\times 0.7$

=

$8.75$

$c{{m}^{2}}$

Therefore, the required area of the sector of a circle is

$8.75$

$c{{m}^{2}}$

.

i

More Material

Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts.

a) Consider the circuit in the figure. How much energy is absorbed by electrons from the initial state of no current to the state of drift velocity? b) Electrons give up energy at the rate of RI2 per second to the thermal energy. What time scale would one associate with energy in problem a) n = no of electron/volume = 1029/m3, length of circuit = 10 cm, cross-section = A = 1mm2

In an experiment with a potentiometer, VB = 10V. R is adjusted to be 50 Ω. A student wanting to measure voltage E1 of a battery finds no null point possible. He then diminishes R to 10 Ω and is able to locate the null point on the last segment of the potentiometer. Find the resistance of the potentiometer wire and potential drop per unit length across the wire in the second case.

A room has AC run for 5 hours a day at a voltage of 220V. The wiring of the room consists of Cu of 1 mm radius and a length of 10 m. Power consumption per day is 10 commercial units. What fraction of it goes in the joule heating in wires? What would happen if the wiring is made of aluminium of the same dimensions?

Two cells of voltage 10V and 2V and internal resistances 10Ω and 5Ω respectively are connected in parallel with the positive end of the 10V battery connected to the negative pole of 2V battery. Find the effective voltage and effective resistance of the combination.

Suppose there is a circuit consisting of only resistances and batteries and we have to double all voltages and all resistances. Show that currents are unaltered.

(i) Consider a thin lens placed between a source (S) and an observer (O). Let the thickness of the lens vary as 2 0 () – α = b wb w, where b is the verticle distance from the pole. w0 is a constant. Using Fermat’s principle i.e. the time of transit for a ray between the source and observer is an extremum, find the condition that all paraxial rays starting from the source will converge at a point O on the axis. Find the focal length.
(ii) A gravitational lens may be assumed to have a varying width of the form w(b) = k1 ln (k2/b) = k1 ln (k2/bmin). Show that an observer will see an image of a point object as a ring about the centre of the lens with an angular radius.
β = √(n-1)k1 u/v / u + v

An infinitely long cylinder of radius R is made of an unusual exotic material with refractive index –1. The cylinder is placed between two planes whose normals are along the y-direction. The centre of the cylinder O lies along the y-axis. A narrow laser beam is directed along the y-direction from the lower plate. The laser source is at a horizontal distance x from the diameter in the y-direction. Find the range of x such that light emitted from the lower plane does not reach the upper plane.

If light passes near a massive object, the gravitational interaction causes a bending of the ray. This can be thought of as happening due to a change in the effective refractive index of the medium given by n(r) = 1 + 2 GM/rc2 where r is the distance of the point of consideration from the centre of the mass of the massive body, G is the universal gravitational constant, M the mass of the body and c the speed of light in vacuum. Considering a spherical object find the deviation of the ray from the original path as it grazes the object.

The mixture a pure liquid and a solution in a long vertical column (i.e, horizontal dimensions << vertical dimensions) produces diffusion of solute particles and hence a refractive index gradient along the vertical dimension. A ray of light entering the column at right angles to the vertical deviates from its original path. Find the deviation in travelling a horizontal distance d << h, the height of the column.

Show that for a material with refractive index µ ≥ 2 , light incident at any angle shall be guided along a length perpendicular to the incident face. Answer:

A myopic adult has a far point at 0.1 m. His power of accomodation is 4 diopters. (i) What power lenses are required to see distant objects? (ii) What is his near point without glasses? (iii) What is his near point with glasses? (Take the image distance from the lens of the eye to the retina to be 2 cm.)

← Previous Next →

More Material

Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts.

Two cells of voltage 10V and 2V and internal resistances 10Ω and 5Ω respectively are connected in parallel with the positive end of the 10V battery connected to the negative pole of 2V battery. Find the effective voltage and effective resistance of the combination.

Suppose there is a circuit consisting of only resistances and batteries and we have to double all voltages and all resistances. Show that currents are unaltered.

Show that for a material with refractive index µ ≥ 2 , light incident at any angle shall be guided along a length perpendicular to the incident face. Answer:

Sign up now and study all subjects for free

Class

Syllabus

Question Papers

Social Media

Apps