An object travels in a circular path of radius r at a constant speed v. What happens to the object’s acceleration if the speed is doubled and the radius stays unchanged?

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BlackTom AI · Accepted Answer

Consider the motion: an object in circular path with radius r and speed v has centripetal acceleration a = v^2 / r. Now the speed is doubled to 2v while the radius r remains the same, so the new acceleration becomes a' = (2v)^2 / r = 4v^2 / r = 4a.

Option 1: 'It reduces to ½ of the original' would imply a' = a/2, which contradicts the relation a ∝ v^2; since v is increased, acceleration cannot halve.

Option 2: 'It reduces to ¼ of the original' would imply a' = a/4, again conflicting with the a ∝ v^2 dependence when velocity doubles; this is not consistent with the formula.

Option 3: 'It increases 2 times' would imply a' = 2a, which would require a ∝ v, not ∝ v^2; the square in the velocity is essential, so this is incorrect.

Option 4: 'It increases 4 times' aligns with the centripetal acceleration formula a = v^2 / r: doubling v yields a' = (2v)^2 / r = 4(v^2 / r) = 4a, so the acceleration quadruples.

In summary, the key idea is that centripetal acceleration scales with the square of speed when radius is fixed; since speed doubles, acceleration becomes four times larger. All other options fail to match the squared dependence or misstate the relationship between speed and acceleration.

SPHY001 Practice Quiz - Unit 06 | LA046

An object travels in a circular path of radius r at a constant speed v. What happens to the object’s acceleration if the speed is doubled and the radius stays unchanged?

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