Correct Answer - Option 3 : 5 m/s
2
CONCEPT:
Centripetal Acceleration (ac):
- Acceleration acting on the object undergoing uniform circular motion is called centripetal acceleration.
- It always acts on the object along the radius towards the center of the circular path.
- The magnitude of centripetal acceleration,
\(a = \frac{{{v^2}}}{r}\)
Where v = velocity of the object and r = radius
Tangential acceleration (at):
- It acts along the tangent to the circular path in the plane of the circular path.
- Mathematically Tangential acceleration is written as
\(\overrightarrow {{a_t}} = \vec \alpha \times \vec r \)
Where α = angular acceleration and r = radius
CALCULATION:
Given that, v = 20 m/s, r = 100 m and at = 3 m/s2
-
Net acceleration is the resultant acceleration of centripetal acceleration and tangential acceleration i.e.,
\(a = \sqrt {a_c^2 + a_t^2} \)
Centripetal Acceleration (ac):
\(\therefore {a_c} = \frac{{{v^2}}}{r}\)
\( \Rightarrow {a_c} = \frac{{{{\left( {20} \right)}^2}}}{{100}} = \frac{{400}}{{100}} = 4\;m/{s^2}\)
Hence, net acceleration
\(a = \sqrt {a_t^2 + a_c^2} = \sqrt {{4^2} + {3^2}} = 5\;m/{s^2}\)