A wheel of circumference 2 m rolls on a circular path of radius 80 m. What is the angle made by the wheel about the centre of the path, if it rotates 64 times on its own axis?
1.6 rad
1.4 rad
1.2 rad
0.8 rad
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CBI DSP LDCE – 2023
The wheel rotates 64 times on its own axis.
Total distance covered by the wheel rolling on the circular path = Number of rotations $\times$ Circumference of the wheel
Total distance = $64 \times 2$ m = 128 m.
This distance is an arc length on the circular path. The formula relating arc length (s), radius (R), and the angle ($\theta$) subtended at the center (in radians) is $s = R \times \theta$.
Here, the arc length $s = 128$ m and the radius of the circular path $R = 80$ m.
So, $128 = 80 \times \theta$.
Solve for $\theta$:
$\theta = \frac{128}{80}$ radians.
Simplify the fraction:
$\theta = \frac{128 \div 16}{80 \div 16} = \frac{8}{5}$ radians.
$\frac{8}{5} = 1.6$ radians.