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A motor car is moving with a speed of 20 m/s on a circular track of radius100 m. If its tangential acceleration is 3m/s2, its resultant acceleration is :
1. 4 m/s2
2. 3.5 m/s2
3. 5 m/s2
4. 3 m/s2

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Correct Answer - Option 3 : 5 m/s2

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 

\(a = \sqrt {a_t^2 + a_c^2} = \sqrt {{4^2} + {3^2}} = 5\;m/{s^2}\)

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