Question

Find the force needed to keep a mass m in a circular path of radius r with period t.

Answer 1

Answer: The correct answer is $F_{c}=\frac{4m\pi ^{2}r}{t^{2}}$.

Explanation:

Centripetal force is the force which is required to keep an object in a circular path.

The expression for the speed in the circular path of radius r with period t is as follows:

$v=\frac{2\pi r}{t}$

The expression for the centripetal force is as follows:

$F_{c}=\frac{mv^{2}}{r}$

Put $v=\frac{2\pi r}{t}$.

$F_{c}=\frac{4m\pi ^{2}r}{t^{2}}$

Therefore, the force needed to keep a mass m in a circular path of radius r is $F_{c}=\frac{4m\pi ^{2}r}{t^{2}}$.

Answer 2

"To keep a mass in circular motion, the centripetal force acts and maintains the motion. Therefore the centripetal velocity or the tangential speed needs to be derived which is the circular circumference divided by the Time. Thereby

$F_{ c }=\frac { mv^{ 2 } }{ r }$

$\Rightarrow v=\frac { 2\pi r }{ T }$

$F_{ c }=\frac { m{ \left( \frac { 2\pi r }{ T } \right) }^{ 2 } }{ r }$

$F_{ c }=\frac { 4m{ \pi}^{ 2 }r }{ T^{ 2 }}.$ "