Length of arc of sector

Q.

A pendulum swings through an angle of ${30}^{\circ }$ and describes an arc 8.8 cm in length. Find the length of pendulum in cm.

1. 14.5

2. 15.1

3. 17.3

4. 16.8

Q.

On a circle of radius $7\mathrm{feet}$, what angle would subtend an arc of length $1\mathrm{feet}$?

Q.

Figure depicts a racing track whose left and right ends are semi-circular. The inner width of the track is 60 m and they are each 106 m long. If the track is 10 m wide, find the length of the track around the inner edge.
(round off to nearest whole number)

1. 301

2. 400

3. 310

4. 320

Q. Which of the following statements are true?

1. Maximum length of the chord is 3 times radius.
2. Shortest distance of the chord from the centre is the perpendicular from the centre.
3. Perpendicular from the centre of a circle bisects the chord.
4. Angle subtended by a chord at the major segment is twice the angle subtended at the centre.

Q.

There is a circular swimming pool. There is a bob at the centre of the pool at a distance of $\frac{50}{\pi }$ m from the pool’s wall. Shyam is standing next to the

wall and holding a thread whose other end is connected to the heavy stationary bob at the centre. Holding the thread Shyam now moves along the wall for 20

seconds and the angle between the initial and final positions of the thread is ${12}^{\circ }$. What is Shyam’s speed in metres/minute?

1. 1

2. 10

3. 5

4. 20

Q.

1. $x$ = $\frac{(y\times \theta )}{360}$

2. $x$= $\frac{(y\times \theta )}{180}$

3. y = $\frac{(x\times \theta )}{260}$

4. y = $\frac{(x\times \theta )}{360}$