Answer :
On doubling the centripetal force on an object in circular motion, the frequency, period and velocity change by a factor of √2, 1/√2 and 1/√2 respectively.
The centripetal force on a object in circular motion is given by,
F = mv²/r
Where,
F is centripetal force,
m is mass of object,
r is the radius of the circle and,
v is the velocity of the object.
If the force is doubled, the mass and radius would not change, only velocity would change,
Let us say the velocity becomes v',
2F = mv'²/r
Putting the value of F,
2(mv²/r) = mv'²/r
√2v = v'
So, on doubling the force,
The velocity increased by a factor of √2.
We know,
v = 2πr/f
Where f is the frequency of the rotation,
When the force was doubled, the velocity was v' and let us say the frequency became f',
v' = 2πr/f'
Putting the values of v',
√2.2πr/f = 2πr/f'
f' = f/√2
So, the frequency will change by a factor of 1/√2.
We know,
T = 2πr/v
On doubling the force, let us say the period became T',
T' = 2πr/v'
Dividing, T by T',
T/T' = v'/v
T/T' = √2
T' = T/√2
So, the period will change by a factor of 1/√2.
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