If during circular motion, the tangential velocity of a body becomes double, then centripetal force becomes:
Correct answer: C. Four times
- A. Double
- B. One half
- C. Four times
- D. One fourth
Explanation
When an object moves in a circular motion, it experiences a centripetal force that keeps it moving in a curved path. The centripetal force is given by the equation: F = (mv²) / r, where F is the centripetal force, m is the mass of the object, v is the tangential velocity, and r is the radius of the circular path. If the tangential velocity of the body becomes double, we can denote the original velocity as v and the new velocity as 2v. We can calculate the new centripetal force as F' = (m(2v)²) / r = (4mv²) / r. Comparing F' to the original force F, we can see that F' is indeed four times the value of F.
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About Angular and Linear Quantities
Rotational motion relates angular displacement, angular velocity and angular acceleration to linear displacement, tangential velocity and tangential acceleration through the radius. Questions use radians, v equals r omega and tangential acceleration, while distinguishing tangential velocity from centripetal acceleration and angular quantities from their linear counterparts.
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